Player skin is not directly tied to active account

In the course of handling MC-12458 , we discovered that the player skin is not determined by the currently logged-in account, but rather is tied to the system account being used.

The user in question has two Minecraft accounts; a main one, and one for map testing. However, the map testing account apparently is using the skin from the main account; this even happens when creating a new map.

Steps to reproduce (requires 2 skinned Minecraft accounts) (Surmised from the situation):
1. Install Minecraft with account 1
2. Play Minecraft with account 1
3. Log in with account 2 on the same system user account
4. The skin might still be the same as for account 1