In general you cannot do this - you need to have grounds of all the devices connected one way or another. The reason is that the voltage by definition is not an electric potential, but it's a difference of potentials between two points (that's what you mean when you say "voltage across a resistor" - it's a difference of potentials between two ends of a resistor). We always assume a point of "zero potential" to be the ground point of our circuit, but in reality this is rather artificial - you could say that the ground is at 100v potential, and it still wouldn't change anything because what we're measuring is a difference of potentials. It's just convenient to say that the ground has zero potential.
You want the reference points in all the circuits (by that we usually mean grounds of the circuits) to be at the same potential, so you need to connect them by a piece of wire - then you cannot say that the ground of one circuit is at 100v and the ground of another circuit is at 200v, because they are electrically connected, so they must have the same potential.
The problem with your circuit wiring was that the preamp and power amp grounds were connected not only by one path (that is good), but by TWO paths: one going straight from preamp to power amp, and another one going like this: preamp->power supply caps->power amp - which introduces a ground loop which may cause trouble (look at the attached image).
When you remove one of those two connections there is still ONE left, so all is good! Ideally you want all of ground points of all the circuits in your amp (power amp ground, preamp ground, power supply ground and what not) connected to one, chosen by you, ground point of your amp (usually the point between the filter caps) by just one path.
Back to the pedal-preamp case: of course it may happen that the pedal power supply is not "floating", which means that it's ground is in some way connected to the mains ground and also your amp common is connected to the mains ground - then you don't need the ground part of the guitar cable going from the pedal to the amp, but it's a rather rare situation so don't cut that cable :trouble
Man, I fell like I'm really awful at explaining anything so I'll just wait for Phil or someone to clear all the confusion I surely introduced :loco
You want the reference points in all the circuits (by that we usually mean grounds of the circuits) to be at the same potential, so you need to connect them by a piece of wire - then you cannot say that the ground of one circuit is at 100v and the ground of another circuit is at 200v, because they are electrically connected, so they must have the same potential.
The problem with your circuit wiring was that the preamp and power amp grounds were connected not only by one path (that is good), but by TWO paths: one going straight from preamp to power amp, and another one going like this: preamp->power supply caps->power amp - which introduces a ground loop which may cause trouble (look at the attached image).
When you remove one of those two connections there is still ONE left, so all is good! Ideally you want all of ground points of all the circuits in your amp (power amp ground, preamp ground, power supply ground and what not) connected to one, chosen by you, ground point of your amp (usually the point between the filter caps) by just one path.
Back to the pedal-preamp case: of course it may happen that the pedal power supply is not "floating", which means that it's ground is in some way connected to the mains ground and also your amp common is connected to the mains ground - then you don't need the ground part of the guitar cable going from the pedal to the amp, but it's a rather rare situation so don't cut that cable :trouble
Man, I fell like I'm really awful at explaining anything so I'll just wait for Phil or someone to clear all the confusion I surely introduced :loco