Maybe Picard was just being polite since he knew it wasn't up to him to decide whether Manheim's program continued to be funded. Picard may have thought that the Federation Science council or Starfleet would probably forbid further experiments as being too dangerous, but agreed with Manheim so as not to be the one to predict bad news ahead of time.
Wrong. Everyone knows there's no money in the future. So it's impossible that his work was funded in any way.
A Matter of Time (season 5): when confronted by a guy claiming to be a time-traveler from the future, Picard declares that he has "examined his credentials" and concluded he's telling the truth. Huh!? What sort of credentials could/would/should a time traveler from the future be able to provide that could be verified in any way? Makes no sense whatsoever.
Since I'm a time traveler from the future I'll show you mine. Ok, I lied. I'm really a time traveler from the past.