LMFAO at that first statement, shows how much you know...
Classic was officially released on Jan 4th, 2001...not mid '02.
Anyways, back to the original topic. It does show last log in days but I think it would just add to those days for rs2 if you do not log into that on the same day. It would be a waste of membership if you don't plan on logging into rs2 and you find out that the account no longer has Classic access though.
Looking at the time frame you gave, did you log in after members was released in Feb '02? They claim to have wiped out all f2p accounts when they closed Classic but there is still a chance you retained items, etc....although a very slim chance.