For anyone who ever wondered why Picard and crew were kept far, far away from the Dominion War....
Tasha: I'm certain I can disable their ship with a phaser burst Captain.
Picard: And than Lieutenant?
Now we know. The Enterprise is faced with a ship carrying a deadly plague which threatens an entire planet. Picard, who is supposed to defend this defenseless planet decides to keep a particular method to himself for no reason. I can see how the writers were thinking "How can Picard come out incredibly awesome in this scene when the solution is obvious?" and the only only answer they could come up with was "make the professional crew of the Federation flagship so incompetent that they can't figure it out on their own". Unfortunately they didn't cover why Picard doesn't tell his crew, or even Haven, so they make him an idiot as well.
This was Picard's second most stupidest moment from the first season.
He wanted to avoid any violence, especially since the intruders did nothing. Things can't always be solved with weapons, you know. And so long as they were on the ship, the illness was confined there, so nothing wrong was done.
Oh and something I only just noticed - Wyatt is Human not Betazoid! So if neither he nor the Tallerians are psychic, how did he and the girl dream-up each others images?
I am sure they had ways, maybe some sort of technology. Technology that can affect one's thoughts is not unheard of.