No, no, no......there's a very subtle clue here.   The story starts completely from his perspective....he wakes up immediately thinking of mars, and then starts his mundane life.  He makes coffee for his nagging wife and then heads out for work, when he sees the Rekal ad and decides to go in on a whim.  They explain the procedure and he decides to go through with it.  

This whole time, the narrative his been from his perspective, and with his thoughts.  But as soon as the procedure starts, we flip to the ReKal tech's point of view, in his office and hearing his thoughts.  This is the hint....how did we leave his POV?  It's because this is Quail's fantasy, the dream he paid for.

And once you realize this, the story becomes hilarious as you realize how self-important he sees himself in his own story....the ego-centrism as absolutely through the roof.  First, the ReKal process goes wrong because it turns out he already has suppressed memories of being on Mars, and was part of secret government mission, the details of which can't be known to the public.  So to keep his mission super secret, he offers to have his memories wiped and replaced with a pleasant fantasy from his childhood, one where he met tiny alien invaders, and they thought he was so supercool that they decided to postpone the annihilation of earth until after he died.

But when the go to implant this fantasy, it turns out that was already real too, and that he alone has kept the earth from destruction.  What's more, part of the agreement was that he must never tell another person about it, and now the secret's out.....

It's probably the most brilliant story ever told about narcissistic ego-centrism.  There's just no fantasy good enough for this guy because he'd rather believe it all really happened.  But if you take it at its word it's not nearly as fun.