I'd say that the original question was too vague to render meaningful answers that are both technically "correct" and realistic/reasonable. The problem is that there are so many other factors that go into playing 1000-rated disc golf. Any answer is based on other assumptions (putting, course selection, placement/accuracy, etc.) Those assumptions that support the "minimum distance" are more important than the distance figure itself.
It's possible to imagine a hypothetical player who can't even throw 260', but plays only pitch-and-putts and aces everything within 250'. Great work, the answer is 250 feet! But that thought experiment is meaningless in the real world. Its only real use is to rhetorically defend a ludicrous answer to a vague question.
Realistically, I could imagine a 1000-rated player who maxes out at 400', has consistent placement on a variety of lines at 350', and putts pretty dang well. Any less power than that would strain my personal credulity.
In response to contrary examples, I'd ask: Are you really talking about the player's MAX distance? Or the distance that they regularly throw/threw on the course with good control and placement?