First Class – not really

The first X-Men movies make a big deal of the fact that the first X-Men seen are also the first students the professor has taught. There is actually a scene in the first movie where Professor X clearly and explicitly says that Cyclops, Jean, and Storm are the first students he ever had.
If we jump to the Origins spin-off, there is no problem – the problem appears starting with First Class, where the first students cannot be more different than those 3 mentioned above. Yeah, there is Havok, who is Cyclops’ brother, but still…
Even Mystique, who is a certified villain in the first trilogy, is one of his first students. So what gives? Did someone erase Xavier’s memory, like he did (unnecessarily) with Moira?
