The law cares about the process you took to get something, not just the final output. Stealing something and then changing some stuff to try to make it not look identical doesn't invalidate the fact that you stole it. I can't download someone's song, strip out the bass line and record my own, and then pass off the new song combining the old music with my bass recording as an original song.
I don't know whether that's what happened here or claim to know exactly what the constraints of IP law for this specific instance are, but "some stuff was changed" does not necessarily seem sufficient as a defense in general. Depending on the exact type of IP law that covers this there are questions like whether the changes were substantial enough to make it an original work or whether the way that the old stuff was used constitutes fair use.
The legal ruling that makes what he does legal even if he didn't get permission (although he does) is about parodies; it's not clear why you think that would apply here. If all he did was change the title and the phrasing of some things, it's doubtful it would be.
The closest equivalent I can think of here would be starting from a blank slate, producing the layout manually to be roughly the same (similar to recording the music from scratch to match up with the original), and then come up with completely original wording that's about something unrelated to the original wording. That doesn't seem anywhere close to what anyone here is claiming.
That's debatable and would have to be proven in court. Weird Al's works aren't really critiques of the original songs so a parody defense would be very difficult to make. One could argue that the humor in his lyrics could have been set to another tune to the same effect, making his appropriation of copyrighted material unnecessary and therefore not fair use.
Weird that you don't mind misrepresenting that intention of mine. Or are you under the impression that you have a telepathic insight into the minds of others?