Yes, if I understand your point correctly: There is no absolute guarantee that all keys won't hash to the same hash key until the keys are absolutely unique! Correct!
However in a practical sense, I think that you are going to be hard pressed to come up with a realistic example for this user's input data.
Of course there is a "trick" here. Even if the hash table has to compare say 16 things to get a result, it is still going to be very fast!
This idea that say 256 things will hash into an identical hash table entry is unlikely. Now "very, very seldom" doesn't mean "never".
But, as the hash grows the probability of this decreases exponentially.