I wonder how accurate the Fargo ratings would be if one poolroom plays solely on 9' Diamonds, and the other poolroom plays solely on 7' Valleys. Would a 650 rated player on the valleys stand a chance against the 650 on a big table?
Yes. That he wouldn't is is a common misconception.
Here is a way to look at it. Suppose East of the river in Metropolis all the tournaments are 7-foot Valleys. And west of the river they are all on shimmed 9-foot diamonds. East players stay east, and west players stay west.
Now don't think of the tournaments as producing Fargo Ratings. Think of them as producing a pecking order.
So after many many tournaments you are East #8 or West #22. And suppose these pecking orders are well established on both sides of the river. Now suppose we have east#10 play west #10 a long set somewhere else. And west crushes east. So west#10 moves up the ladder and beats East#9 and East#8 and East #7 and splits with East#6.
Now for Fargo Ratings West#10 and East #6 are going to end up with the same rating, maybe 650. Basically from this the entire east list shifts down. This kind of coupling happens all the time a little here and a little there such that someone who plays primarily on 7-foot Valleys doesn't somehow get extra credit.