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The reason that the negative post got so many votes down is that it was made by Andrew L, who a.) is not in a position to give that kind of advice, and b.) mixed his advice with political comments about the mathematical community and professors and top schools.
I agree that the advice is overly optimistic, but it's not my place to say it.
I agree that for such questions there is a trend towards optimism, but I'm not sure how (or whether it is wise) to counter it. In the context of advising an anonymous stranger online (whose mental state is unknown), I think most people are unwilling to give advice that is too negative. I think that one can presume that the person seeking the advice is all too aware of the pitfalls of their situation, and people are naturally reluctant to amplify the questioner's pessimism in too open a manner and so add to their distress. Thus the more negative aspects of people's advice are couched in somewhat nuanced terms (as various comments above note).
If one wanted to address the issue, one possibility would be to add a remark to the FAQ making the obvious point that it is difficult for strangers to provide detailed career or personal advice, and hence that consulting MO on such matters is going to lead to imperfect and incomplete advice at best.
It's probably true that one gets slightly over-optimistic advice on MO; after all, the random people on the internet are going to fill in the details they don't know about you in an optimistic way. Since they don't have any reason to think you can't work on multiple projects, they don't want to be so uncharitable as to think you can't. I'm not really sure what you could really do to correct this, other than telling people not to seek advice that depends pretty strongly on their talents, interests and life situation from people who know none of those things.
As for Andrew's answer, it got voted down because it didn't make any sense (unsurprising, since it was written by someone without experience as a Ph.D. student or advisor). You shouldn't start from the assumption that your advisor is ruthlessly exploiting you to advance themselves in their field (we're not chemists), and I don't think many advisors would be very troubled by you saying you were thinking of trying something different and asking them for advice. But of course, it all depends on context, which we don't have.
Just to reiterate my point: I think a big part of the problem is trying to get advice from people who don't know enough to pitch it at the correct level. Look, for example at this question which I resulted in the OP getting good and appropriate advice, because he actually provided details about his situation.
That reminds me of the anecdotes that I've often heard about Mathematicians being among the first ones cut from the Jury interviews by prosecutors. I haven't had the chance to serve jury duty in the States, so I can't vouch for the veracity, but it is said that the mathematicians often get too hung up on the "prove" part of "prove beyond reasonable doubt".