AFSIK, when they use the term "fully open", they mean open dataset and open training code. The Olmo series of models are the only mainstream models out there that satisfy this requirement, hence the clause.

> We go beyond just releasing model weights - we provide our training code, training data, our model weights, and our recipes.

https://docs.allenai.org/#truly-open

Yes, and that's why saying this is "the best" is a tautology. If it's the only one, it's obviously the best, and the worst, and everything.