Explaining the reason of radically more accuracy while using different set of hash functions instead of same set of hash functions on some operations
A possibility is that algorithm A is randomized, but at least one of the following holds

the source of randomness used is poor (e.g. tends to repeat), and using several sets of hash functions fixes that, merely by introducing more of the randomness necessary for accurate results (whatever that means) of the overall procedure.
there is no randomness fed into the input of at least one of the hash functions in a set, therefore changing that hash function adds some of the beneficial randomness.