But my point is that if the code itself remains under the GPL, how does publishing an alternate version of it "undo" the GPL considering all the rights restricted by the second license would still be available under the GPL?

I think your argument is: sure, I'm distributing over here with way fewer rights than normal, but it's also available over there with all the rights, and it's the exact same stuff and so that's good enough. And I see why you'd think that, it's not completely unreasonable, but it's just not how the license is worded.

It's either GPL with all the rights that entails, or you can't (legally) redistribute it at all.

Now, if you own the copyright you can give out as many parallel licenses as you want. But pidgin & libpurple have been around for 20 or more years and have had many, many contributors, and they have to explicitly give up their copyright or consent to the license change to do what you propose. That's theoretically not impossible, but it's a lot of work.

This is why some projects require you to sign copyright-assignment agreement before they will take your patches—it gives the project more flexibility to change the license in the future.