Something being "as real as any memory in your head" doesn't mean it has to be a memory of an actual event. I have strong memories of very, very, vivid dreams and I'm able to separate them from reality. (Unless I really did once get paired with a beautiful woman by aliens, taken to an underground bunker they had built and kept in protection during an earth-wide space disaster, and then used with her to repopulate the Earth.)
So Quaid would have woken up with all of these memories of this stuff having happened but he still also remembers going into Rekall and ordering the "Ego Trip" and the various aspects of it so he also
knows that everything that happened to him between entering Rekall and waking up there was a dream. A very good, very vivid, very relaxing dream, but not real all the same.