It's interesting to note that this is almost exactly how it works in some role-playing games.

Suppose that we have Xandra the Rogue who went into dungeon, killed a hundred rats, got a level-up and now is able to bluff better and lockpick faster, despite those things having almost no connection to rat-killing.

My favorite explanation of this phenomenon was that "experience" is really a "self-esteem" stat which could be increased via success of any kind, and as character becomes more confident in herself, her performance in unrelated areas improves too.