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For us at the retail end of the spectrum, this is most certainly true, and it is most useful for us to look at pricing this way, to determine relative under/overvalue.

Therefore the BSOPM (as proxy for whatever model):

Input ===> Share price, strike, expiry, risk free rate, dividend, Volatility

Output ===> Option price

Becomes:

Input ===> Share price, strike, expiry, risk free rate, dividend, Option Price

Output ===> Implied Volatility

I would love to find out if someone, somewhere in the trading universe (initially at least) inputs volatility to get the output price.

MM's I have listened to say no, that outside bids/asks determine the vols. It seems like a bit of a chicken or egg thing to me.

I suppose it matters not, as far as we retail traders are concerned.