You seem to think that I'm arguing that collisions might be a problem. I'm not. I'm raising a point of English usage. "Unique" is not the right word to use in this context; "distinct" is correct.
If a set has a single member, that member is unique; e.g., 2 is the unique even prime number.
If a thing is different from all other things, it's distinct.
I think that you're not catching my point, and recommend that you look up the word "unique" in a good dictionary, preferably of mathematics.
(It's tautological and uninformative to say that any x is the unique member of the set of things equal to x. And it's simply incorrect to say that any member of a set with multiple elements is unique wrt that set.)
If a set has a single member, that member is unique; e.g., 2 is the unique even prime number.
If a thing is different from all other things, it's distinct.