The first question, "is the Higgs mechanism how elementary particles get their mass?" is now essentially answered. Whether or not the Higgs boson is a single particle or part of a hierarchy of related bosons is almost irrelevant to the answer of this question.
The second question is "is there new physics at the TeV scale?" If there is, then there are additional bosons related to the Higgs in some models like supersymmetry. However, it is not required that there be additional bosons or that that they be easily measured. Other new particles might be more accessible. On the other hand, there might not be any new physics at LHC energies at all. This question is what will take time to answer.
The uncertainty is about the structure that exists beyond the standard model. Some sort of Higgs is still necessary in almost any extension to this model, which is why everyone was so damn certain it would be found.
My understanding from the statement is that they know there is the effects of a Higgs has been observed. But that this isn't necessarily the Higgs which fits into the Standard Model. I understand there are other models which may be considered but I thought that there were specific conditions which would satisfy the Standard Model.
We know that the standard model is "wrong" -- it breaks down at high enough energies. But it's valid at lower energies; it works for the stuff we can actually observe. And it requires a Higgs field to make sense.
If they discover a particle that fills this role, that's discovering "the" Higgs. It doesn't matter if it turns out that the Higgs sector is more complicated; the fundamental prediction of the standard model has been vindicated. Even though everyone kind of expected this, its still a big deal!
So if a pop science article says that the Higgs has been discovered, they're not really being sensationalist in their wording. Working physicists would say the same thing.
(They might be a bit off in pointing to this particular announcement as the discovery, of course! The bbc seems to have the most sober coverage of this sort of thing: http://www.bbc.co.uk/news/science-environment-21785205)
Now, it's quite likely interesting stuff happens before that point! (Such as the extra Higgs suggested by supersymmetry.) And there are also other, complicated reasons to suspect that the Standard Model breaks down, to suspect that it is really what we call an "effective field theory".
That's all ignoring issues like dark matter or the neutrino mass, which are not predicted by the standard model. But it's kind of interesting that the model (in a certain sense) naturally limits its own predictions.
God Particle Found! News at eleventy eleven!eleventy!
When I was a bartender, I would often consume tidbits of popular sporting events or news just so I could hold conversations with my patrons. I had absolutely 0 interest in who crashed at Daytona that day.
In my experience most people don't form their opinions based on the totality of current knowledge and keep adjusting them in some Bayesian fashion as more info becomes known. Rather they make up their minds based on something (could be their knowledge of currently accepted facts, could be what they were taught growing up, could be just what they think makes sense, etc..) and then simply scan for confirmatory data, or simply don't pay any attention because they already have it 'figured out'.
Thus if you already believe in god and heard that scientists had discovered the 'god particle' you would likely say 'see, I knew it!', if you didn't believe in god and saw the same thing you would say 'I am skeptical, let me read this article', and you would walk away saying 'that is just a name, it has nothing to do with god, who still doesn't exist'. So really I guess both sides win, and we all lose, or maybe I am just too cynical.
Sensationalism where?
"It remains an open question, however, whether this is the Higgs boson of the Standard Model of particle physics, or possibly the lightest of several bosons predicted in some theories that go beyond the Standard Model. Finding the answer to this question will take time."
I find this to be a pretty important distinguishing factor. Not only will it take a while before they really do know, but it may not, in fact, be the Higgs so many have been searching for to fit into the Standard Model.
Many news sources are already claiming that the "god particle" has been found.
[0] - http://press.web.cern.ch/press-releases/2013/03/new-results-...