Who says Chekov was being honest? Just because a character says something, doesn't necessarily make it irrefutable fact. Perhaps he was getting techy about his approaching 30th,
Well, in TOS Chekov was intended to be the "young guy" of the group, the inexperienced one who all this is new for. Were he really approaching 30 he'd be in the same basic age range as Sulu and Uhura, and therefore not very young or inexperienced. And I'm fairly certain the intent when Adonais was written and filmed was that he was giving his actual age.
To be honest, Chekov's presence is one of the worse examples of the "Nero's presence changed the timeline" handwave excuse's we get in the Abramsverse. There's no real reason Nero showing up and destroying the Kelvin should have motivated Chekov's parents to have a child sooner but there we are.