The original phrasing was "stored properly, (i.e. bcrypt)". That's including the hashing as part of the 'storing'. Bcrypt has a size limit, but a size limit is not the same thing as truncating. It's broken code on the front end that truncates instead of doing something like sha512.
Bcrypt spits out a string, that the caller must store, somewhere. I presume the parent post means that Bcrypt "stores" in its output string a value that, for all practical purposes, varies reliably with the same salt but different plaintext.
