It drives me nuts how many people confuse QBR (a proprietary stat created by ESPN) with Passer Rating. Like the OP.
To your point though, I agree about passer rating. It's entirely arbitrary. In order to get a 158.3, you need to have at least 77.5% completion percentage and 12.5 yards per attempt. Why 77.5%? Why 12.5? Just because?
It's very silly on its own, but it's still a useful "at a glance" stat.