I don't know much about electronics. I've always wondered why the exact voltage doesn't matter much. Those words were paraphrased from either Hugo or Rob if I recall correctly, but I never understood why. Anyone care to explain? In layman's terms

I'll try.

Because very little in the empeg actually runs directly off of 12V. All the digital circuits (and hard drives) are 5V. I suppose there might be some 3.3V stuff too (I haven't really looked for it, and don't recollect seeing it).

Anyhoo, the 5V supply is created from the '12V' line by a regulator. Basically any modern (*) power regulator is a specialised form of integrated circuit - ie it has a lot of internal components to make it do what it does. One of the things that a modern regulator does is accept a wide _range_ of voltage inputs and provide a stated output with a stated precision. Truthfully, that is its entire purpose in life, and a 5V regulator that could _only_ provide exactly 5V from _exactly_ 12V would be useless - any noise (ripples, spikes, notches, glitches etc) on the 12V input would be passed through to the 5V output (by definition).
So the manufacturers specify and design regulators to provide a stated output with a stated maximum noise figure from a stated range of input. For example the 78M05 linear regulator (common as muck regulator chosen as example) is spec'd to have a maximum of 50mV ripple on it's output as long as the input it at least 8V. This is useful - many digital circuits will only operate correctly with a supply voltage of 4.75-5.25V, ie less than 500mV ripple on exactly 5V, so we know that a 78M05 would be a good candidate for such circuits.
It will actually operate down to 7V, but that maximum ripple number doubles to 100mV. Still good enough. The 2V difference between the minimum input and the 5V output is what the circuitry internal to the regulator needs as overhead to operate.
The 78M05 will operate with an input range of 7-35V. I have no idea where the 35V figure comes from, possibly an internal component breakdown voltage. I've never been particularly bothered about finding out.

But the 5V circuits are not the whole story in the empeg. The display uses 60V to drive the VFD, and that has to be created from the 12V too. We have some analog electronics that I haven't really looked at. And don't forget that the 12V is switched for the Remote Amp line too. Not only that, but the empeg's 12V input has a transient suppressor to eliminate ignition spikes that are common in automotive systems. Any of these elements could be the cause(s) of the 12-16V range quoted by the guys.

I'm speculating that the Remote Amp line is the reason for the 12V figure (who knows how various amps would respond to less than 12V?), and that the transient suppression is the reason for the 16V number.

(*) Modern in this context meaning approximately post 1980.

I've always wondered why the exact voltage doesn't matter much.

To answer in a completely different manner...

Why should it?

If I asked you for a 12V power supply, I bet you could find one.
How about if I asked you for a 12.0V power supply?
12.00V ?
12.000V ?

I have this wonderful Tektronix bench power supply that I can set to be 12.00V. It has a great 4 digit LED display to tell me so. It's guarranteed to provide line regulation to under 0.03%. Its list price is ~$900 (Gotta love ebay). It's a great piece of kit. But since its display accuracy is limited to 0.5% of reading, that could really be 11.94V or it could be 12.06V, and I wouldn't know the difference. Until I got out my 0.2% accuracy mutimeter, in which case I would then know that it was somewhere between 11.976V and 12.024V.
Understand? Even with some reasonably decent electronics gear, I cannot accurately quote any better than 12.0V.

With that in mind, can you imagine the havoc that would result if consumer electronics needed an accurate 12.0V supply? How much more would the power supplies cost to produce? (Each one would require calibration). How many people would get frustrated due to voltage drifting that occurs with temperature, load and age? How much would the tech support cost? Frankly, requiring such accuracy from an external supply would be incredibly bad design.

Fortunately, most consumer electronic equipment is easily tolerant of 5% voltage variations in their rated supply, if not more, so has no problems with your dirt cheap 12V supply that may really be 11.4V or 12.6V.

I'll admit that 12-16V is a large range to see quoted. Remember that sometimes things get simplified in the marketing and documentation stages (Can you imagine Jane NoBrain asking in RatShack for a 12-16V adapter? Can you imagine the employee's response? "Dur...dunno what that is")
That 12-16V figure did come directly from engineers.