I have read your example multiple times, and still don't think I get it.

Are you essentially trying to say Table[3][1 << 15] can happen to be equal to Table[3][0]? Because that's the only case the 2 Fragments can be equal, assuming the other entries of the table are the same.

Isn't that essentially the same as finding a collision in the 3-words hash function (that generates Fragment)?

Does this property make collisions more likely? Since all the table entries are randomly generated, I would think that makes this function more uniformly distributed, not less?