I think a more exact comparison would be, say, a t-shirt with a fluffy Google logo and the text changed to say "Poodle". It's not really saying anything about Google, it's just using Google-related imagery mashed up with dog-related imagery.
The example I like (even though Weird Al seeks permission and so doesn't need his fair use rights) is Weird Al's "Smells Like Nirvana" versus "Fat".
Smells Like Nirvana is necessarily about Smells Like Teen Spirit and Nirvana's video for that song. It has lyrics like "We're so loud and incoherent / Boy this oughta bug your parents". If you make that song using Dolly Parton's "9 to 5" as the basic structure, now it's just nonsense. I believe the parody exception would apply to "Smells Like Nirvana".
"Fat" isn't about Bad or Michael Jackson. Jackson wasn't fat, the character he's portraying isn't fat, the song isn't about food, there's no connection. It's just funny lyrics to the same structure. If you do this to Bon Jovi's "Living' On a Prayer" that's funny too, a few people have done so, "Standin' On a Chair" for example. If you did that and get wealthy, expect Bon Jovi's label to demand most of it, parody rules don't help you.
With the T-shirt that says "Poodle" like a Google logo, you don't need their style. You could use the Ford logo, or the McDonalds logo, or a dozen others, doubtless you'd say you wanted a double-O - does Moodle (a VLE) have a logo? I bet they do. If you wanted Google's logo 'cos it's recognisable that is not a protected reason.
As I understand it this Supreme Court decision was pretty narrow, and doesn't get into the parody question anyway.