Even this is both overstating the case, and contradicting the evidence, alas:
1) We know Picard started out his starship career on the
Stargazer, but we don't know exactly when. That is, no mention of "He first came aboard in 2333".
2) We don't know how long Picard was associated with the
Stargazer in the sense of a sum total of years, either. That is, no mention of "20 years".
3) We know
Stargazer was his first, but that once-cut scene from "Measure of a Man" states there was the
Reliant, too. And back when he was but Ensign to boot! This eats into his
Stargazer years, but again we don't know how badly.
To postulate a moment where Jack is Lieutenant and Picard Ensign is not particularly difficult - the two could be of roughly the same age, and Picard is the one with the skyrocketing career. To add Cadet Howard takes a bit of doing, as Beverly supposedly enters Starfleet Academy late enough to graduate in 2350. Even if he spends eight years at it, doing all of her medical studies in Starfleet, 2342 should see Picard at higher rank...
They likely referenced Tapestry for Picard and Family for Jack Crusher, with their rank insignia reflecting accordingly.
Well, yes - the specific images are copy-pasted from the respective Memory Alpha pages. Jack's is the first image that comes up at his page.
Timo Saloniemi