You mentioned that the person "behind the camera (not the front) that is most important". Most important implies that it is more important.
I just wanna say it may not be always the case, althou in general it makes sense. consider the example that I mentioned, even the professionals may still require that the camera can properly AF for him to get the picture that he wants. A beginner, with top end gear, anyhow fires few thousand shots at 10fps at a sports event on Full Auto.. compare with a professional with many years experience, always at the right place at the right time who anticipate the moments with solid accuracy, armed with low-end gear and F5.6 lens, who captures the moments with 50% OOF pictures (mis-focus), or missed the moments due to shutter lag, or camera unable to lock focus hence never open shutter, or underexposed noisy pictures. Who will have a higher % of good pictures?
While there are certainly examples of award winning pictures taken with PnS, but it will depend on the situations. If the pro can take his time to compose and the PnS can lock focus and fires, sure, the person is more important.
But in cases where speed, accuracy of AF, response time, rate of fire, high ISO performance etc etc are critical, the equipment may actually matters more than the photographer.
And, as you have mentioned too, the "right" equipment. And the "right" equipment may mean high end gear, in examples like sports photography. So "right" equipment may still be more important than "pro" PG sometimes.