The thing is, if the time traveller posts his claim, he's already changed what people would've normally posted if he wasn't there.
So he can't know at first, what someone would ask. So he would have to travel back in time EVERYTIME someone asks a question, if he wants to answer them before they're gonna be asked.
Or he has to wait until all have asked their questions, gather them and then travel back to post them before they're gonna be asked.
The problem with this could be, that if he's only arrived in our time ONCE yet and gathers all the answers, he'll have to leave again into the past to give our past selves the answers before THEY post them.
But from our perspective this would already be in the past. That's why we can't get an anser from the time traveller. Only our past selves.
So, this means, as soon as a TT makes his claim, he would have to post our answers directly, without asking us any questions.
Because if he DOES ask us, then this means he will have to make another travel into the past AFTER he collected our questions.
Which in turn means, we won't enjoy the pleasure of getting our answers, since he had to leave to present our former selves the answers.
Sadly with this argumentation I opened another door for hoaxers, who can be defended with: "Well, he can't give US the answers, since he's still collecting, but he'll travel back and give them to our former selves!".
But then again this shows that it wouldn't be of any use to us if he would only need us to make questions.
So think of another proof you can give us immediately without the need of a second time jump!
I want the proof in the here-and-now of THIS timeline, screw the others, damnit! :D
P.S.: This only holds true for "certain" time travel timeline types, of course.