I'm not sure if we're conflating them, and I'm a also not sure that it matters. Both problems are vulnerable to attack via practice, so if they are a bad signal or a bad attribute, a dedicated person can overcome them.

Now, I would have to temper the previous statement by saying I have great admiration for anyone who goes to the trouble of learning my language, considering I haven't troubled myself to learn theirs. The prior statement was not meant to be a judgment on people with accents, only an observation under the hypothetical closure of PG's statement being true.