Not sure, I never really looked into it--just remember reading somewhere that Trout was granted special consideration for some reason or other, probably related to the fact that he is really freaking good. Let me see if I can find out what the official reason is.
Edit: Oh, I see. So the rookie eligibility rule (since it was constructed by people who I do not trust at all and who frequently make decisions that make no sense) use ABs, not PAs. So Trout had only 123 ABs and is eligible from that perspective. Apparently it came down to a technicality in terms of how many days he was on the roster:
In order to retain eligibility for the Rookie of the Year award, a player can’t have more than 130 at bats, or more than 45 days of service time on the active roster, excluding September. Mike Trout has 123 at bats. Mike Trout has something like 38 days of service time on the active roster. Mike Trout, though, is not eligible for next year’s Rookie of the Year award, Major League Baseball has told the Angels.
The reason for this is a little bit of a quirk in service time rules. When Trout was called up in July, he was added to the Angels’ 40-man roster for the first time. When he was sent down, then, he was what they call optioned. When you’re optioned, you aren’t on the active roster, and you don’t accumulate service time, EXCEPT you must be optioned for at least 20 days in the season for that option to count. (An option lasts all season, no matter how many times you are sent down.) Since Trout wasn’t on the 40-man roster before he was called up, he hadn’t previously been optioned, so his time in Double-A before that didn’t count. He was then called back up after only 17 days, and spent the rest of the year with the Angels, so his option didn’t technically happen. “The service time has to go somewhere,” says the Angels’ Tim Mead, which means it counts as major league service time. From the Collective Bargaining Agreement:
If a Player is optionally assigned for a total of less than 20 days in one
championship season, the Player shall be credited with Major League
service during the period of such optional assignment(s).
Mike Trout, then, actually is credited with 55 days on the active roster, not counting September.
So it's not as bad as it initially looks. Still, most rookies wouldn't have received that special exception--I think the Angels pushed really hard for it.