A 940-rated Am plays Open in one C-Tier event, lucks up and wins $20 last cash, and he should never play Am the rest of his life?
The distinction between Pro & Am is quite fuzzy. Most of our Pros aren't professionals; they don't make a living, or even earn more than their entry fees. Our Ams are hardly amateurs, winning stacks of plastic and other merchandise.
The reason for the under-970 rule, for those with shorter memories, is that at one time accepting cash doomed you to the Pro ranks for life (unless you petitioned the PDGA). Players would rise to the point where they could test the pro waters. Some would plateau in the mid-900s and find themselves in limbo; they could pay high fees, play Open and almost never cash....or they could quit playing tournaments. It was called "Move up---move up---move out."
So some players never left the Am ranks, for fear of getting trapped in the Pro divisions.
One effect of the current rule is that better Ams can step out of the Advanced division to try Open. When they choose to, they make room for those who stay back in Advanced, and add to the pool of Open players (and to the Open purse). A pretty good deal, all around.