I would guess that it has something to do with the fact that most tapes are recorded at a relatively lower level. And the gains on internal amp in the head unit is set accomodate a signal that has that sort of input voltage. So when you turn up the output on MP3 player up and send it through the tape player it's recieving alot more powerful signal than normal thus causing the head unit's amp to clip.

Of couse this is just my hypothesis...