Nope, I have not run into this problem. In fact GT6 is the best game I have ever played when it comes to User BGM. If you have played NHL 2010-2014 you'll know how terrible User BGM can function in the hands of lesser developers.
I have 3301 songs at the moment running on shuffle in GT6, and the variety is as it should be. Very good shuffling.
The one gripe I have is that GT6's User BGM isn't working in all modes. For example, If I play online and host my own lobby/room the User BGM never works and never has. The game just goes back to the standard OST songs.
Strangely enough the User BGM works perfectly If I race in someone elses lobby/room o_O
But never at Monaco though, no matter what the circumstances.
Dead annoying really.
Actually there is one more thing, I dislike how the game needs to change track/song every time you install a new part or repaint something or generally performs any task on the car.
Really when tweaking a car to my liking I hear the first 15 seconds of twenty different tracks because each new action prompts a new track to be played.