Lots of superstition and old wives tales here. I've not studied square taper crank spindles in particular but they are a subset of machine assembly in general. Whether it's the square taper or the threads, coefficient of friction plays a major and analogous role in both cases. At the end of the day, with a bolted joint, you want a deterministic axial preload, for the integrity of the joint. In the case of the square taper crank spindle, the bolt preload does two things simultaneously: it indirectly determines the radial preload on the square taper (via the jacking effect of the axial preload on the radial preload), and it ensures that the bolted joint has sufficient axial preload to preclude loosening and backing out of the fastener, due to cyclic stress reversals.
Now the radial preload on the square taper is there for two analogous reasons; one, to pre-load the crank arm in hoop stress so that the added hoop stress due to the jacking effect of applying pedalling force to the crank arms is relatively small, so that the cyclic stress reversal amplitude due to pedalling is relatively small compared to the DC hoop stress, and two (a byproduct of one) the possibility of relative motion between the crank and the spindle is nil, so that fretting and/or loosening will not occur.

Lubrication, per se, is a bit of a side issue. Both the aluminum crankarm, and the fastener, have upper limits of stress that they can withstand without yielding plastically. Typically, in both in a bolted joint, and in this special case of a square taper crank, plastic yielding is bad, but there are definitely exceptions in specially designed bolted joints, and it's possible there are in square taper cranks, though I doubt it.
The thing is, the specified torque, whether a bolted joint or square taper crank, is only valid with the specified lubrication. One without the other is an incomplete formula. The specified lubrication (and prior preparation, e.g. cleaning) determines the coefficient of friction that results in the conversion of torque to axial preload (in the case of the bolted joint), and the conversion of axial preload to hoop stress, in the case of the square taper joint.

So, with the incorrect lubrication or the incorrect torque, the joint is compromised one way or another. Here are the possibilities:

1. too much friction, correct torque - the preloads will be less than designed, which can cause loosening of the bolt or the crank, fretting of the crank, and probably worst of all, increased fatigue damage to the crank due to higher cyclic stress amplitude
2. correct friction, too little torque - same as 1
3. too little friction, correct torque - danger of plastic or complete failure of crank or fastener - may result in early fatigue failure of crank, or make the assembly impossible to tighten properly after being disassembled
4. correct friction, too much torque - same as 3, this is probably what happened to the OP.

Clear as mud? Good... I thought so.