Why is a clamp meter unaffected by nearby wires?
Imagine that the return conductor for the red-wire (the blue-wire in your picture) is a million miles away. You would probably agree that it has negligible effect.

Now as the blue return wire is brought closer, the localized magnetic field it produces helps the red wire's magnetic field (on the left) but it also produces an opposing magnetic field passing through the "ring" on the right.

The two opposing fields always cancel to produce the same net effect: -



The magnetic field from the red-wire not drawn for reasons of clarity.