If you can apply it without getting any on the carpet, might want to put a penetrant on it and let it sit out in the sun for a while to heat up and try it. Fluid Film & Kano Kroil are two of the best I've seen at freeing up seized metal parts. Also, from the picture that looks like a Springfield Spring-Lock pedestal that's missing the release button. Can you see a black plastic piece inside the pedestal itself?
I couldn't see anything in that little hole where it looks like the release button would be. At the same time, it's very difficult to see in that hole since it's so close to the carpet. I can certainly try to look in there again today after work. But you're right, it does look like that's what it would be. Just not sure how I could release it without anything in that hole.