Some very good posts above. Quite a lot of this seems to be common sense, but it's really bad how much common sense just flies out of the window in relation to this.
Obviously the sensible (and the *only* sensible) assumption if having sex with a person you don't know well enough to trust is that they may be +. Unless they were tested yesterday (no, scrub that, *even* if they were tested yesterday) *and* they are being 100 percent honest, there's a risk. It's *our* responsibility to decide whether we will take that risk, and to do the things (condoms, PrEP) that reduce or eliminate it. And to campaign, wherever we can, to make those things widely available and widely understood. It's a scandal that anyone is infected nowadays, and it's a scandal based on the fact that in many places gay sex is still stigmatised. Can you believe that in England, on the NHS, you can't just get PrEP by going to your GP? Can you believe that I recently met a general practice doctor who didn't even know what it was?
But *because* that's the sensible and the only sensible assumption, we should not be stigmatising people who are + and say they are by treating them as pariahs. These are risks for all of us that we can all manage and take responsibility for. The insistence (which I'm afraid is all too common) that + people should be responsible for "warning" the "clean" guys (look at the language, and how it drips with judgment) is completely off beam. I daresay that apps like Grindr think they are being responsible encouraging people to "share" this information, but really it's sort of the reverse: it encourages a totally false sense of security (where none is justified) and a totally false judgmentalism (where none is justified). When we stigmatise those who are + we are just contributing to the vicious cycle in which people -- often especially young vulnerable people -- put their head in the sand and the problem ends up getting worse. If we could get everyone who needs it on PrEP, get everyone to test often, and get those who test + onto the right drug regimen quickly we could more or less lick this thing, and we won't do that unless these outdated and ill-informed and moralistic attitudes are finally trashed. We'd still have a deal of work to do on other STDs, but at least that would be progress.
So to answer the OP's question. If someone asks for only bareback sex, it means they want only bareback sex. No point speculating whether they are or are not +. They could well be. They might not be. It's not worth trying to figure it out, and you can't. You have to decide if it's a risk you are prepared to take.