You might consider pointing out to your "network engineering professional" that the propagation delay in copper is LESS that that of fiber (in most cases).
The difference between difference between the two is on the order of 0.1C. So in round numbers, that's 0.3 ns/m. If we imagine the distance between you and the provider is 10 km, that's an additional 3 uSµs delay. That's at least 3 orders of magnitude below whatever other delays there might be. You'd need very expensive equipment to even measure it.
This question might be helpful too.