Yes, and in addition to union stipulations, if any...
...another question would be how much, say, lighting direction the principal person did. If he did a fair bit, or a lot, I'd credit him as Cinematographer. If there was little-to-none, then he is "Camera," or "Camera Operator."
Of course, you might have had a different person altogether that was the director of photography... in that case, that person is the "Cinematographer," irrespective of whether he actually operated the camera. Then, your cameraman would be "Camera" or "Camera Operator."
The other guys would be "Additional Camera," or even "Second Unit Camera," depending on exactly how you were working.
Fantastic Plastic Entertainment, Inc. fantasticplastic.com