Neither one explains if we’re talking about legal authority or being considered authoritative for purposes of scientific inquiry.
Neither one is intended to. You have all the information you need to answer the question honestly. I would note that the aim Weinberg has stated would require legal authority or some other power so strong that it was at least equivalent. It's likely, however, that you realized that before I pointed it out.
Instead of trying to mold the parameters of the question to your liking, why don't you just answer it?