There's another non IE language you need to know about. It's called Estonian. It really is different from Hungarian and Finnish ~ at least its speakers say so.
The closest ancient language cognate to the Sa'ami languages is called Sumerian, and it, in turn appears to have originated among the Dravidians. Lots of history in that one just now being discovered.
In retrospect, I think my old teacher may have meant four language GROUPS. Still, as you pointed out, wrong, but slightly less wrong than four languages...lol