The Android OS has the ability to move apps to the SD card. A secondary ability of this feature is for a Developer to decide if he wants the App to be movable. He has three possible settings that I am aware of at present.
1) Do not allow.
2) Allow moving after install from Market.
3) Install directly to the SD from the Market if the SD is present.
I believe Angry Birds is hitting item #3 and encountering a problem. By turning off the SD card, you force it to the phone internal memory.