It's far more nuanced that that. Have had Aetna HMO but the company I was working for in Dallas, there was not a single provider in Brazos county that would accept it. Have had BCBS PPO of both IL & TX. While most would take not all doctors/procedures were covered at in network rate. Have Humana PPO now, what would be considered platinum under obama care and some things are just crazy. If I have my quarterly lab work drawn at my SJPA doctors office my share is $212, but if I go to any lab, it's $7 because of the bogus hospital admission. Also have had BCBS high deductible plan, and some providers are willing to negotiate fees and other not. A local hospital imaging group would only let me pay the BCBS URC rate, but another would let me pay the cash price and not file. The difference was over $2000 on a MRI.
It absolutely matters what insurance, and recurring medical needs you have when you pick a doctor.