This was actually evidenced recently when Indians accused China of utilizing a 'bearded man', and the Armenians accused the Azeris of utilizing 'Pakistanis'.
There can be only two mutually exclusive interpretations: either SSG was actually deployed in these cases, or it wasn't. If it was, that corroborates your points above.
But even if SSG wasn't deployed, it shows a deep psychological impact on the enemy's mind. All Pak Army has to do is to officially announce its support, and enemies start seeing 'bearded guys' and 'Pakistanis'. This is only possible through an established reputation resulting from a long history of successful deployments which are unknown to general public but very well known in the military circles.
@Metal 0-1