The reason it's confusing is because they're using irrelevant and misleading terms.
Tanks need to be O2 cleaned if they will be filled using a method called "Partial Pressure Blending". This involves adding 100% O2, then topping off with "hyperfiltered air", which is also known as "Grade E Modified".
Tanks do not need to be O2 Clean if they will be filled using any type of continuous blending, where the nitrox is already at the desired percentage (32%, 36%, etc.) when it is added to the tank. This type of nitrox does not have to meet the standards required for Partial Pressure Blending. This is what they are using on the boat, and is why you don't need O2 clean tanks to get a nitrox fill on the boat.
However this also means that if your shop does Partial Pressure Blending, and requires an O2 clean tank, and you get a fill from someplace that does not meet the "Grade E modified" standards (the boat), your tank needs to be re-cleaned before the shop that does PPB can fill it again.
The reason for this is because tank contaminants can cause a fire or explosion when filling using PPB.
While the boat says that you do not need an O2 tank, what they're not telling you is whether or not it will still be O2 clean after you get a fill. It's possible but unlikely that their air meets the Grade E Modified requirements. In fact, a lot of boats have a hard time even meeting the standard requirements.
Terry