This is a bug found in the game.
Solution: 
Get away from the door, go right, and kill the clone. Kill the guard mounted on a machine gun on top of a prison window. Go back, and it should be open. If this doesn't work, go to another section of the level, such as the library, and then go back to the Funfrock HQ section. The door should be open.
I did encounter this bug myself, and using the above method always worked for me.
Thanks for pointing this out! If this doesn't work, please let me know.