While 1 in 650,000 hands does sound like a rare occasion, consider that I am a fast player, probably doing at least 800 hands an hour. That brings it closer to (I am rounding here) 1 in 810 hours of play. I usually play at least 4 hours in a day where I play, or 1 in 200 or so days of play. Since I live in Vegas, I might play as much as twice a week (again this is an average because some weeks I don't play and sometimes I might visit somewhere like Tahoe where I am playing 3-4 days in a row and more than 4 hrs a day), let's say 100 times a year in 4 hour sessions, which might put me "due" for a dealt royal once every two years. Of course the variance would say it isn't at all odd that it took 5 years in between two dealt royals instead of 2 years. The "average" might be approximately 2 years, but the reality of statistics is that you can't predict when they will show up. You could get them back to back or 20 years apart.
But the reality of being a player is that when it is 5 years between dealt royals you can feel pretty bad.