Until they find a way to prove that the FP interpreter or compiler (usually written in C!) cannot corrupt it's own stack, every other claim of proveability is built on sand.
Sure, if the compiler has a bug, you're screwed. But how is that any different than the non FP case? It would be heaven-on-earth if we only had to worry about compiler bugs. Just compare how many bugs you find in you're own code, versus bugs in perl. There's a good reason why there are fewer bugs in a compiler than other code written in that language. Because more people use the compiler in more different ways. And most FP compilers (common lisps, haskell, ocaml, etc.) are self-hosted if for no other reason then it shows the compilier writers are willing to eat their own dog food.
-- All code is 100% tested and functional unless otherwise noted.