The mere fact that an assertion has been made is, in fact, evidence.

Well the evidence here isn't really "the fact that it has been asserted" but "the fact that it has been asserted in a context where truthfulness and authority are usually assumed". The assertion itself doesn't carry the weight. If we're playing poker and in the middle of a big hand I tell you "I have the best hand possible, you should fold." that isn't evidence of anything since it has been asserted in a context where assumptions about truthfulness have been flung out the window.