[jml7c5]

The problem is that a hash is not even close to a one-to-one mapping of input data <-> output hash. There are a truly enormous number of possible 4 KiB strings that can produce a given hash. Assuming SHA-1 is evenly distributed, there are 2^(8*4*1024) / 2^160 possibilities (which is 2^32608). You could find some 4 KiB piece that works, but it would almost certainly not be the original. Even if your torrent had a single file with a single missing 4 KiB piece, and even if you had a machine that could spit out every configuration that would pass the hash check, you'd still have 2^32608 theoretically valid files to test.

(Note: I'm not taking the time to think the specifics through so my math may be incorrect, but the conclusion that the search space would remain huge is sound.)