Ok, me and my friend Fireeye (youtube) discovered this:
You know in these two glass cubes containing a lot of corrupted cores just before the final battle ween you and Wheatly? Look in the claw, and you’ll see another core whith a white “iris” that sends a glow to the other cores. So, now, if it allready were in the claw, why didn’t GLaDOS use it first? Why did she drop it to pick up the Space Core instead??? The only logic answer is that the white core wasn’t corrupted and wouldn’t do a shit to Wheatly.
EDIT: With Wheatly it should be the fifth core…