Not on being unable to encounter the same hash in any random other string, no - only on not having collisions in output of the function that generates a hash from an input string, from different inputs.
In your interpretation, security seems deemed broken as soon as the system encounters the same string, by any means, which to me seems more like an attack vector in itself -- if one can inject things that will make critical parts throw an exception, should your injected code trip on a secret key, I don't see how that would be a good thing.