Most of the time, that isn't true. Hardware failures are (barring quality control issues) independent, hash collisions are not.
For example, if you assume your hash will not have collisions, and design your hash table without any mechanism for coping with one, and it happens to have a clash on "Jones" and "Smith", your address book app will become unreliable for a rather large fraction of your users.
But at the scales we're talking about, it won't happen to have a clash on "Jones" and "Smith". This won't be a hash table - this will be things like a git commit hash, where generating 1/ns is likely to give a collision in 3 years, before which the storage required just to store hashes is in the yottabytes.
For example, if you assume your hash will not have collisions, and design your hash table without any mechanism for coping with one, and it happens to have a clash on "Jones" and "Smith", your address book app will become unreliable for a rather large fraction of your users.