A good question, but here's an even better one: if architecture must be true to its era then how come we've got so many examples of buildings that were modified from their original form into monstrous imitations of whatever happened to be popular in some later era?
Maybe "must" is too strong of a word. Ideally it should represent its time. This often does not happen--either because the building is deemed to be sadly out of date and is "modernized". Look at the MEC for example, stuccoed over in the '50s to resemble a shoebox, then partially revealed 10 years ago.
In a way, that building embodies all its eras: it's original architecture, the 50s modernization and the recent rehab and rooftop addition are all visible to the eye.