But how will you know you found the real password and not a different string sharing the same hash?
Well...erm...if it looks like a password, smells like a password and works like a password, then does it make a sound when it falls and nobody is there to hear it? I'd say yes; at least on mondays!
edit: But, ok, you are absolutely right, if the user is lazy enough to use the same password on different sites, it is a good thing, one cannot really find the original password.
Even though with my luck, all my different passwords for different sites probably have the same MD5-hash...