The phrases pick the door's lock and a self made key are not accurate however it does appear that an orangutan called Fu Manchu did use a tool to unlock a door and escape at least twice.
In lock-picking circles, the technique of using a credit card to push the bolt out of the way is known as shimming a lock. The tool used to fit through the small gap is known as the shim. I'm not really sure if using a wire to unhook a latch could be considered shimming, but it's certainly not picking, which is a technique used for pin-and-tumbler locks and the tool was not a key.
An article linked from the page you supplied in the question describes his actions like this:
"Fu Manchu pulled the door back from its frame. Taking a piece of wire from his cheek, he then tripped the latch, much the way a thief might slip a credit card between a door and its frame."
Keepers confiscated the wire. But the escapes earned Fu Manchu honorary membership in the American Association of Locksmiths.
The Time article describes it like this:
First, the young ape climbed down some air-vent louvers into a dry moat. Then, taking hold of the bottom of the furnace door, he used brute force to pull it back just far enough to slide a wire into the gap, slip a latch and pop the door open. The next day, Stones noticed something shiny sticking out of Fu's mouth. It was the wire lock pick, bent to fit between his lip and gum and stowed there between escapes.