For a total store order to be meaningful of course it implies that loads are also non visibly reordered. If a store falls in the forest but nobody is around to load it, was it really ordered :)
Tbf you could say stores happen in order, and loads can happen out of order unless you fence. Personally I don't understand why we need such strong ordering constraints for weakly ordered reads—istm you can go much weaker and maintain sanity.
