The license commercial software uses gives you no rights to do much of anything, yet nobody thinks Adobe owns photos edited in Photoshop.

Exactly. No one thinks that with Adobe. Yet as the original poster pointed out, people do have confusion with open source licenses.

Why should granting more rights change that? It makes no sense to me.

Rights granted with GPL aren't strictly more to the person deploying the GPL code.

And GPL already calls out what is covered. Source code. It's incredibly clear.

The GPL definition of source code is the following:

The "source code" for a work means the preferred form of the work for making modifications to it.

Honestly, I'm not sure exactly what that means. I have a good idea, but if deploying with it, I'd certainly get a lawyer involved.