Some noted key points from the video ...
Player connected to Jaymod server without issues (does not prove he is not running a cheat)
Player connects to silentmod server and is banned on detection of possible cheats
Loading screen (unlike on jaymod) is loading missing (player missing custom pk3?) or replaced textures (server admins that re-use other people's custom packs sometimes leads to this)
Assuming player is not cheating. Install fresh copy of game from splashdamage to a new directory. Do not install punkbuster service. When running the 1st time be sure to disable punkbuster. Delete the pb.cfg or any reference of punkbuster in the player's /etmain/ folder. Be sure to at least open game to enable profile before connecting to any server.
Have the player download the map, mod and any custom pk3 files to ensure the player is ONLY using files the server is looking for on the client. This rules out any server errors like the client is not getting directed to download all the required files. Server admins usually overlook this because they have the master copy that built the server 
If the loading screen fails to load as before then I would investigate further. There are known hacks that can replace textures (such as replacing walls with glass in pak0.pk3). Not suggesting your friend is cheating but this might be what the AC is detecting (but I didnt write the AC so no clue what Im saying here lol).
A workaround is to find his player ID# and mark it in the default.cfg (on the server under mapconfigs). Something like unban 3
If he is cheating you would be permitting it - so understand the risks.
Edited by sageone, 18 October 2016 - 10:17 PM.