I think it has more to do with the fact that there has to be some term to describe the concept of "model which has weights that are openly accessible"

Like, that's just a logical thing to call it. I don't believe anyone is making a judgement on the intelligence of the reader to call it "open weight" when it refers to weights that are openly available.

"Open source" would be a more appropriate term to describe a model which also includes the training source.