No that’s not true, even UK has heavy restrictions on their use. And this is under 2 Prime ministers!
What I see instead is that UK is allowing US bombers to make multiple bombing runs on Iran from its bases.
Afaik there is zero cooperation from France and Spain, and Germany has been difficult enough that Trump has threatened to close the Rammstein base, which is the biggest air base USA has in Europe.
This is mostly true for Spain, even then there were a couple of military airplanes in support roles landing and taking off from Moron. So it seems the claimed airspace closure was more of a gentleman's agreement rather than a strictly enforced prohibition.
But France and Germany absolutely did allow support airplanes in support roles to use their airfields. The exact nature of the operations is not known but it's probably to do with recon and maybe refuelling. The reason bombing runs were not on the table is mostly because these countries don't host any US military bases with suitable runways to support heavy bombers.
Greece allowed a US carrier to dock and repair in between combat operations.
Bulgaria and Romania explicitly allowed the US to use their bases for refuelling and recon.
All of this for a war that is poised to inflict heavy damage on European economies via skyrocketing energy and fertilizer prices. If European countries truly were "independent and free" allies of the US, they could just say no, like Spain - after all this is clearly not a defensive war and doesn't benefit them in any way. Instead we got a bunch of face-saving claims and a permission to perform whatever support operations are needed.