Here's another interpretation
If all loads are L-C (Line to Common Grounded Conductor, or "Noodle"), then:
Ã˜A, Ã˜B and Ã˜C may be all at 200 Amps, and the Common Grounded Conductor will also be at 200 Amps (neglecting THD >10%).
If L-C loads are all Resistive, and each Line is at 200 Amps, the Common Noodle may not be drawing too much Current!
This would be a very rare occasion!
Anyhow, the load Current flowing in a single Conductor will , of course, flow through the Fuse (or Circuit Breaker) also. This is the reason for the OCPD.
Measuring "I" (Amperes) using a Clamp-Around Ammeter (such as the mentioned "Amprobe") on a Conductor, shows the load current on that Conductor at that certain location.
The real deep question to throw back at your co-workers (for a really indepth think-a-thon), would be what's the total L-C load at the Transformer (or main service if Transformer is not reachable).
Figure first by calculating the L-C loads, then check levels via Ammeter at various points prior to checking at the supplying point.
Sweeten the deal with some friendly wagering - such as the closest to the right answer(s) gets a free lunch (paid by the rest of the participating crew!).
Also, consider what Bjarney has mentioned about non LCL loads!
A 20 amp circuit may have 20 amps for eternity, 30 amps for an hour, 40 amps for a few minutes, 100 amps for maybe 15 seconds, and so on!
Discussions like this at work are very good ideas! Best way to learn is to toss ideas around and verify answers with referenced items - such as was done in this forum!
Keep up the activity! Just don't waste too much work time doing this stuff! (gotta throw out that Foreman Attitude once in a while!)