The 3 modules share a common 0V ground, so the probes from each module are referenced to this 0V, of course he can use his probes from one module to another.
We do this all the time,
Example: a PIC project, a scope, signal generator and power supply all on the same bench using a common 0V on the system.
He is not talking about separate power supplies, you are just causing confusion.!
I am not talking about separate power supplies.
You are not looking at the bigger picture.
How do you know all the probes will be referenced to 0V?
This isn't a signal genrator or 'scope which will definitely have an input/ output referenced to 0V. It's a current meter which can measure both positive and DC currents so will probably have its probes biased at some other vcoltage to obserb the common mode rating of the input amplfier.
I doubt the current probes will be and even if they are it's potentially dangerous trying to measure current on the same circuit as the 'scope's ground is connected to. Suppose one of the probes is 0V (in which case it'd need a negative rail)? Measuring the current through the positive rail would short circuit the supply.
For example, suppose the current meter's amplifier stage looks like the one shown below.
What happens if the current probes are connected to 0V?
It won't work!
Even worse, what happens if the current probes are connected to 9V?
The op-amp is destroyed!
If the circuit being measured is not connected the same ground as the current meter, it doesn't matter because the meter's power supply will float at whatever voltage is required but as soon as you connect the 0V to 0V of the circuit you're measuring bad things can happen.
The problem is, we don't know what the current amplfier looks like so we can't say whether it's safe or not to measure current on the same circuit as the 'scope's ground is connected to. Of course, if it uses something like a hall effect sensor, then it won't be a problem but we haven't seen the schematic so we don't know.