As an American, I find it amusing the same way I find it amusing when someone points out the sky is blue, or the Earth is round.
That's simply not true, and a drastic oversimplification of American politics.
It is true that there are two mainstream America political parties. However, anyone is free to run as an Independent or under the banner of any other party they choose, whether that be the Green Party or the Libertarian Party. Here is an example ballot, showing that more than just Mitt Romney and Barack Obama were on the 2012 federal election ballot: http://www.sos.ms.gov/links/elections/home/tab1/GE12%20Sampl...
As you can see, the Constitution Party, Libertarian Party, Green Party, and Reform Party also appeared on the ballot.
It is true that voters seldom vote for people outside the Republican or Democratic parties. (Two notable recent exceptions are Bernie Sanders, formerly Democratic Socialist who switched to Democrat, and Joe Lieberman, Independent) Why is this? Because for the most part, people are happiest with one of those two. How's that possible? Because there's an enormous amount of political range within a party. Basically anyone can up and announce that they're a Republican at any time, and that's that. Ron Paul and John Kasich can be in the same party and nobody blinks an eye. That's why you hear expressions like 'Tea Party Republicans' or 'Blue Dog Democrats' or 'Southern Democrats'. There's a lot more variety in the party than you see in European parties and party members are free to do basically whatever they want while in office. They don't have to vote in blocs.
At the same time, Americans vote for damn near every position imaginable. Federal government is largely divorced from most people's everyday concerns; you get a vote for President/Vice-President, two Senators, and a Representative. The policies that affect the average American most are legislated and executed on a local and state level, not a federal level. States have enormous power in America politics. And take my state, for example: I get to vote for Governor, Attorney General, Lieutenant Governor, State Auditor, Secretary of State, State Treasurer, Agriculture Commissioner, State Senator, Insurance Commissioner, Public Service Commissioner, Transportation Commissioner, Supreme Court Justice, District Attorney, and House Representative. On the county level, which is also where an incredible amount of decisions are made, I elect a Supervisor, Constable, Sheriff, Justice Court Judge, Tax Collector, Tax Assessor, Chancery Clerk, Circuit Clerk, School Board Member, Superintendent of Education Coroner, and Prosecuting Attorney. And the more local you get, the less party matters at all.
There isn't a democracy problem in America: most of the most important decisions - education funding, infrastructure development, criminal laws and prosecutions, law enforcement, taxation, utility management, etc - are made on a state level or a hyperlocal city or county level. The reality is that the federal government has comparatively little to do with most people's lives, beyond getting a federal income tax return, the military, Social Security, and Medicare.
The problem is with the people.
It is in practice quite true even if it is not nominally true, and not only that it is true, but the connection between it and the particular kind of poorly-representative electoral system the US has been established by comparative study across democracies.
> There isn't a democracy problem in America
Yes, there is, largely to a very poorly representative electoral system. Lots of elections doesn't make a well-functioning democracy, that takes elections which produce governments that are effectively representative.
Can you explain in what sense American government is not representative?
People freely choosing to vote for people that you don't consider to be in their best interests does not make a government unrepresentative.
There are a few factors that impact representativeness - gerrymandering and the ineligibility of felons and illegal immigrants, for instance, but all-in-all that impact is pretty minor. In particular, of course, at a local and state level, those impacts are reduced along with the scale. There's an unwarranted hyper-focus on federal government because it's the most visible and affects the most citizens, but for most people's day to day lives, it is the least important level of government.
If Americans have a divisive, gridlocked federal government that produces results nobody likes, that's the natural consequence of a divisive, gridlocked populace that doesn't know what it wants (lower taxes! more social security! balance the budget!), not un-representative government.
While 'Winner Takes All' is one way to do representative voting and checking that item off the list, it's one of the worst ways to be representative. CGP Grey has a series of videos on different voting systems and their pros and cons on youtube - start with this one, which goes through the ways 'winner takes all' drives towards worse representation: https://www.youtube.com/watch?v=s7tWHJfhiyo
Another issue that Grey doesn't mention is that electioneering in the US is so constant and expensive, that politicians can rarely afford to speak in-depth to people without money to donate. It's a subtle effect and not really corruption, but a result of having to endlessly chase the dollars in order to electioneer.
The US has a representative system, no-one's arguing against that. But is it satisfactory or unsatisfactory?
State and local elections are often not winner takes all, but two-round voting. (Really, more than that, if you want to cheat and count the primary election and possible run-offs there.)
Because it produces outcomes where the distribution of power in government does not follow the distribution in the preferences of the electorate (even the distribution as expressed in voting, which is already distorted by tactical accommodation to the known features of the electoral system.)
This is problem stemming largely from the use of single-member winner-take-all elections by majority/runoff or plurality rules, as is the case for most legislative (and many other) elections, and which is compounded, at the federal level, by distribution of representation disproportionately to population (obviously in the Senate, but granularity results in significant variance in district size for House seats, as well.)
Arend Lijphart's Patterns of Democracy provides pretty good coverage of both the degree to which various modern democracies have representative government, the structural features that are associated with effective representation, and the effects that those variations in effectiveness of representation have.
> People freely choosing to vote for people that you don't consider to be in their best interests does not make a government unrepresentative.
True, but America, nevertheless, among modern democracies has a notably poorly representative government.
> There are a few factors that impact representativeness - gerrymandering and the ineligibility of felons and illegal immigrants, for instance, but all-in-all that impact is pretty minor.
Gerrymandering actually has a lot less impact on representativeness than it gets credit for (but it having any significant effect is a product of single-member, winner-take-all districts, which have a very large effect on representativeness, even outside of gerrymandering.)
> In particular, of course, at a local and state level, those impacts are reduced along with the scale.
No, the scale might be reduced, but the effects of gerrymandering and disenfranchisement, such as they are, are not reduced at local scale (and may actually be exacerbated, depending on the locale -- there are locales above and below the national average for distortion from any of those sources.)
Additionally, there are systems used at local scale (such as multiseat elections on a Vote for N system, with N winners) that are frequently used in local elections that are more hostile to effective representation than single-member, winner-take-all districts.
OTOH, the effects of unequal allocation (at least for legislative districts) are reduced at the state level.
> If Americans have a divisive, gridlocked federal government that produces results nobody likes, that's the natural consequence of a divisive, gridlocked populace that doesn't know what it wants (lower taxes! more social security! balance the budget!), not un-representative government.
Well, no, its a product of a combination of unrepresentative government and a Constitutional system deliberately made to have many veto points, which means if the distortions that effect different institutions work in different directions, the result is gridlock.