If the 1000 subjects are chosen well, it's mathematically legitimate -- and the authors give appropriate error bounds based on the ratio of the sample to the population. More detail here:

http://en.wikipedia.org/wiki/Sampling_(statistics)

Furthermore, the author is implying that this is a condition specific to Americans when there is no evidence comparing US citizens to other nationalities in this regard.

"Americans think" doesn't imply "only Americans think." I don't see anything in there saying citizens of other countries are different.

"It doesn't look like _you_ beat your sig. other, this time." (or any other time).

While not saying that this person did ever beat them before, someone might make that connection.

So "Americans think" (and others might think, but we have not queried them). It's at least ambiguous in that it allows for easy misinterpretation.

Most polls you see on TV are around this sample size... it's often that you see 1000 person polls on news networks (look at the small print on the screen).

That's true but its still pretty funny and interesting nonetheless, I'd estimate that on a larger sample it would still be over atleast 30%