I guess it means that the particular bag can be used more than once, a handful of times perhaps, before being thrown out. Not all reusable bags mean perpetual reuse, some just mean more than once.
I don't see how these bags made it better at all - in fact it's much worse. The bags will be used (or discarded) exactly the same as the cheaper ones - it's just wasting 3x the amount of plastic.
It just seems like a policy designed to reduce trash was twisted in it's interpretation and will actually generate way more trash. It's absurd!
I think that rules like this are fairly common in rules providing for reusable bags and banning single-use ones.
What matters is cost (environmental as well as production) and incidentals like whether they can suffocate children or sicken people by providing pathogen habitat, or even aesthetics (disposed on highways).