While I can agree with the OP that it is annoying when people conflate opinions and facts, I’m not sure that the OP’s definitions of them is good enough. I think the P=NP question is an excellent example of why objectivity isn’t the best line between them because, as that poster said, it is objectively either true or false, but no one knows the answer, but a lot of people have opinions about it (though, overwhelmingly on the not equal side).
I think the thing is, they have different meanings in different contexts and people have a tendency to use them as attacks. If, for instance, someone doesn’t like someone’s argument, they might emphasize that their opponent’s position is just an opinion. Or if someone wants to strengthen their own argument, they might assert it as fact. If someone doesn’t want to go through the effort of defending their position, they might say it’s just an opinion, etc.
At what point do facts and opinions cross? Using UHC as an example, a fact would be stating statistics based upon how other groups implemented it and what their results were, but the moment that one asserts that, because of those statistics, it will or won’t work in a particular setting, it is now opinion. It is opinion based upon facts, but it is still opinion. It doesn’t become fact until after it is implemented and there are statistics to analyze, but even then “good or bad” or “worked or didn’t work” are placing value upon facts within a particular context, and that makes those evaluations opinions.
Or to give probably a slightly less charged example, consider something like sports where the facts are utterly indisiputable. You can compare someone who is widely considered to be an all-time great against someone else in the same position who is average. You may be able to bring up tons of stats that all show the all-time great as superior, and even though the overwhelming majority of people will agree with you, you’re still placing value upon the facts. In short, a lot of people seem to believe that a widely held opinion, even one that is unanimously held, somehow is fact; it isn’t. That’s a logical fallacy.
That said, it does get confusing when statements are made about opinions. For instance, saying player A performed better than player B in stats X, Y, and Z is a fact. Saying player A is better than player B because of his performance in those stats, is an opinion. However, stating that someone believes that player A is better than player B, based on those stats, is a factual statement about an opinion, but that it is a fact, and even if it is true that someone hold’s that opinion, even if he is an expert, that doesn’t mean that it logically follows that the assertion of the opinion is a fact or that it is true. That’s also a logical fallacy.
Either way, it seems to me that usage of both terms gets fuzzy, and popular usage as emphasizers or de-emphasizers has made it worse, not too unlike how “literally” can now be used as an emphasizer too, thanks to popular usage. So, I personally avoid using any of them unless I’m clearly using them in their denotative sense; otherwise it just creates ambiguity.