...Although it's IMHO much more interesting that, in the alternate circumstances of the war timeline, they don't. In fact, they put up quite a bit of resistance against this "noble" thing at first.
But that would contradict the Guinan backstory from ``The Child'', where she says --- presumably without lying to Wesley since what would she have to gain by that other than messing with Wesley's head? --- that she hadn't met Picard until she came on board.
Which goes against the literal truth of "Time's Arrow" anyway. From Guinan's point of view, she unambiguously first met Captain Picard in the 19th century. That is, unless "Time's Arrow" and "The Child" take place in subtly different timelines.
Wes: "[People say] that you knew Captain Picard when he was on the Stargazer."
Guinan: No, I never knew the Captain till I came onboard."
Guinan could be telling an outright lie to hide the existence of time travel from the general public (including nosy kids who actually probably already know quite a bit about time travel), or to hide this specific incident from Picard until he has had the chance to go back in time. Guinan could also be more subtly disingenious, perhaps saying she had Picard figured out all wrong originally (didn't "know" him), or omitting the fact that the two will first meet when Guinan comes aboard some vessel (perhaps the
Enterprise where a time-traveling Picard resides, long before the 19th century. Whatever the explanation, she ain't telling the truth, the whole truth and nothing but the truth there.
Timo Saloniemi