Michelangelo was mostly told to 'paint the ceiling', what he painted was of his own devising. For sure he would probably not have been paid if he painted a forest scene but there is some evidence in his own hand that his inspiration was mostly scripture (the OT).

I'm pretty sure the reigning pope approved of the design, both from an execution perspective as from the content itself.

But if he had done the job according to the normal way of decorating ceilings in that day we likely would not be having this discussion. It really is a masterpiece.

Why not? They would be the genesis of the idea, after all. It just seems bizarre to me to say that religion did not urge him to do this, which is the usual meaning of 'inspire.'