Every class which is low for itself is closed under complement, provided that it is powerful enough to negate the boolean result. EXP, which is closed under complement, but is not low for itself.
NLOGTIME can negate boolean result, it just can't pass whole input into oracle, and passible size is log(n), on which size it needn't an oracle. NLOGTIME is also not closed under complement due to EQUALITY.
Is it some misunderstanding or wrong wiki?