Air Traffic Controller here. You are correct.

There are many airports that are just a runway and have CTAF (Common Traffic Advisory Frequency) where pilots advise each other of their position, heading, intentions, etc.

ATC can give clearances to aircraft landing and taking off from such airports, but the clearances only apply in controlled airspace, usually starting 700ft above the ground. ATC can also make sure there are no other IFR traffic for aircraft requesting clearances, but if it's VMC (visual meteorological conditions), there could be VFR traffic for the IFR aircraft that ATC is not talking to.

Even taking off from an uncontrolled airport don't Part 125 commercial ops still require ATC to operate?

Any flight above 17999 ft in class A airspace requires an IFR flight plan. IFR requires controllers for the clearance, release, and approach clearance. Probably what he means....

Most Jets and planes people have experience with would be flying at those altitudes.

FYI:

Civilian flights in Class A airspace (at or above 18,000ft in most places) require an IFR clearance.

State flights can fly "due regard" (VFR) in Class A airspace.

In Hawaii, there is no Class A airspace, and I once controlled a civilian aircraft flying VFR at FL210 (21,000ft).

I never said they didn't. Commercial flights must fly IFR, which means they must receive an IFR clearance prior to takeoff.

Commercial airliners do not take off in non-towered airports.

Yes they do. I have issued clearances through Flight Service to such aircraft.

There are many Commercial flights every day to non-towered airports. In backcounty Alaska this is the norm. Clearly you have a big-city bias in your thinking.

OK, that's fair. Didn't consider Alaska which is known for these requirements.