The data is potentially recoverable from hard drive wiped with zeroes solely because the underlying medium is capable of storing more information - the 0 overwritten by 0", 0 overwritten by 1, 1 overwritten by 0, and 1 overwritten by 1 are, potentially, distinct states of the platter.

Synapses, on the other hand, store synaptic strengths on molecular scale, where if the state information is lost, it is completely gone, as the molecule which can be either in the state A or state B does not have state of "B but it used to be A" or "B and it used to be B".

edit: bottom line is, the energy barrier between different values has to be considerably larger than kT for the data to persist at all . The synapses already store the data at an energy level low enough that if you go much lower - for the analogue of residual magnetization on a drive which is much less energetic than original magnetization - you're in the region where the data simply can't be stored.