No, this is wrong. Private Medicare plans fully replace Original Medicare. If you are on a privately-managed Medicare plan, you receive none of your benefits from Original Medicare (the government-run program).
Unfortunately, you're still subject to some of the care delivery restrictions that Medicare sets, which means people moving from privately-managed plans (without Medicare) to Medicare Advantage (privately-managed Medicare plans) will typically experience a drop in coverage, because private insurers tend to be more forgiving with these limits.
> they want to use a doctor that is not participating in the medicare program
I'm not sure what you're referring to here. Though yes, one of the big advantages of Medicare Advantage is that it's dramatically easier to find in-network providers, even for Medicare Advantage plans that don't cost anything out-of-pocket above what Original Medicare does.