I think the remark you want is on page 361 of the Princeton Companion to Mathematics.
Edit in response to a comment - the paragraph in question follows:
The ABC conjecture has many other marvelous consequences; for a delightful survey, see Granville and Tucker (2002). In fact the ABC conjecture and its generalizations can be used to prove so many things that I have joked that it is beginning to resemble a false statement, since a false statement implies everything. But probably the ABC conjecture is true. Indeed, though a bit harder to see, the Erdős-Ulam probabilistic argument can be modified to provide heuristic evidence for it, too.