I really don't think so. I thought that about myself for a long time but when I tried my hardest to think positively and ignore it - still there, still bad.
I often get migraines at the same time of day. If I don't wake up with them...I get them between 1-3. It's weird and I have no idea why, but it sounds like your friend is the same way. I think it probably has to do with what he eats for lunch and how much sleep he gets at night. It is also easy to get into a rebound cycle with too much medication - to the point where your body expects the medication at a certain time. I actually had to quit year round swimming when I was younger because I always got a migraine towards the end of the school day, and it was an after school program.
Try to be supportive of your friend, I really doubt that it is in his head