We don't know that Jack knew from the beginning what Sydney's status was (not having read what Sydney read--we don't know what was in that document). In fact, he was imprisoned at about the time that the video was taken that furnished the proof that she survived. I would consider it a bit of a "cheat" on the part of the writers if they decided that Jack knew for sure what had happened to her (if he had reason to suspect she had survived but did not know what had happened, that's something else again). The fact that Kendall chose his moment for "full disclosure" when Jack was conspicuously absent is interesting. I also note that when Sydney escaped the Covenant and came to the CIA, Kendall kept her from everyone (Vaughn conveniently involved and watched, Dixon sworn to secrecy, Jack--he claims--off on some undercover mission), leaving himself (with his ties to the DSR) with exclusive access to her services. Interesting, no? Then, consider that he stepped in and attempted to seize complete control (through arrest) of Sydney before (via the prophecy). There are some indications of a power struggle . . . my thought is that both Kendall and Jack (and probably others, like Sloane) want to control Sydney--the significant consideration being that Jack's the only one in the game protecting Sydney's interests (heck, she could hardly protect them herself when she was a baby!). I think Kendall is an important player here. But, hey, this is all conjecture.
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