Setting a texture (using either local or global command) on an player will cause other players that had the original player out of their render/view distance to not have that texture when they get closer.
This seems to happen when the player that has the texture set on them has different clothes when the bugged player last saw them
I can't provide evidence, but I was testing by teleporting the players to eachother a few seconds/minutes after.
If I had one pair of clothes on and was near the other client, went a far distance and changed my clothes, then set a texture (either locally for the other client or globally), the texture would never apply for the other client, but would for me.