Interesting discussion - on the concept of metal memory, I think things are being stretched (pun intended) in the discussion. A couple of points -
Any closed tank or vessel that is being pressured up is being stressed, and there is a resulting strain (or, in simple language, the vessel wall is stretching). The classic stress-strain diagram for any material shows from zero pressure to some higher pressure the strain change is linear with increasing pressure - this defines the elastic region. At that specific higher pressure (which is unique for each material, wall thickness, etc.) the slope of the strain change breaks over dramatically and basically the material is stretching fast enough that continuing to pump into the vessel does not result in any more pressure - this defines the plastic region. Of course at some point it falls apart as it stretches too thin. Within the elastic region as pressure is released the material returns to its original shape / size (strain is reduced with decreasing stress). But within the plastic region the material has been permanently deformed and it does not return to its original shape / size when pressure is released. I believe the comment about metal memory is referring to the elastic region of the stress-strain relationship.
Back to the tank fill and hydro test, these pressures are obviously well within the elastic region. So why do we need to hydro the tank more than once if we are never going to have a working pressure that high? Because, even ignoring any potential negative effects of corrosion, the stress-strain relationship is different when the material undergoes cyclic loading than static loading. That difference is the material is weakened due to being subjected to stress cycles - and when we are filling (pressurizing) the tank, using the air (releasing pressure), and repeating over and over we are subjecting the tank wall to cyclic loading. So the stress-strain relationship for the tank material is changing the more we use the tank. This is a fundamental reason for the need to hydro the tank, although corrosion (if present) will certainly worsen the weakening process in and of itself.
Back to the original question - does overfilling harm? Well, the fact that the pressure is higher on an overfill means that for that cycle the stress is a bit higher, even if it is only for the period that the air in the tank is hot. So IN THEORY it is speeding up the weakening process a little bit. But in practice I don't believe it makes any real difference, the big effect is the stress cycling that occurs from as tanks go from near-empty pressures to full pressures over and over.