I understand where you're coming from, but I think that strict reading of the statement, that the identity is the result of the influence is materially different to what you're talking about. That is, I think "authentic" transness is popularly considered an innate characteristic, you are born this way even if you don't realize it until later in life. If the identity is the product of social influence then the implication is that it is not entirely innate, that you are claiming to have been born a particular way, but only because you have been misled by outside forces. Put another way, you can be told about transness online and realise you were always that way, but then the identity isn't the "product" of the social influence. (I know this comes down to fiddly definitions, and reasonable people may differ.)