Why are you assuming that? You can compare hashes ("does the encrypted version of what they entered as a new password equal any of the encrypted previous passwords").
If by hash you mean a one-way hashing system, then he did say significantly different and not just different. You couldn't do that with any common one-way hash.
You're correct, I didn't understand what he meant by significantly different until you pointed out because I have never encountered a system that didn't allow me to have a "similar password". However, I have encountered ones where my new password could not contain previous passwords, so unless they are hashing each component of my password and comparing this probably does indicate clear-text storage.