That is not a very precise way of describing the uniformity of hash functions, and it's not actually true. For example, if my input has some element with 50% probability, then the hashed output is going to have some element with at least 50% probability.
But this is well-known, and because it's well-known, no sane cryptographic system cares that hash outputs leak information that way. For example, look at PBKDF2, HMAC, or various asymmetric key authentication schemes.
