Somewhere in the middle of "A Matter of Time" episode of Star Trek: The Next Generation, curious as always Riker says, that Berlinghoff Rasmussen (the time traveler) could be some kind of impostor like many they've seen before.
Captain Picard contradicts him claiming that time traveler has all the credit he need, that he's proven his words and that all circumstances verify his story thus far.
How can that be? Picard, as well as rest of the crew and episodes viewers has nothing save the time traveler's own words to prove his story. The entire episode is set on the course that someone suddenly appears, says what he says and suddenly everyone believe that they're speaking the unvarnished truth?
Is there anything that I have missed that supports Picard's claims and actually confirms the time-traveler's story?