I disagree with that, and so did the Supreme Court justices. Companies put out "side products" of their own all the time. Think about Tesla's flamethrower, or their tequila. I could easily imagine a liquor company putting out some good-natured pet products that imitated their primary brand.
If you study economics for any length of time you will realize the majority of human misery is driven by market power abuses restricting human ingenuity, pushing labor prices artificially, etc. Copyright, patent, and trademark explicitly increase market power substantially and so it is very dangerous to do what the supreme court did, as the fundamental test for these things should be "what is the minimum we can do to solve x?" where x is a problem like brand confusion, product safety, etc. What was done in this ruling was to push us even further from the minimum and it's a very bad thing for society.
I don't see any problem with this ruling whatsoever. It says nothing about parody for non-commercial purposes. The dog toy owner was specifically trying to leverage JD's brand for his own economic benefit. And it's not like a patent, where patent owners try to remove the ability to make something that sometimes isn't even that novel in the public sphere.
Slippery slope arguments are incredibly weak here if you look at the actual content of the ruling.
It's as if instead of the band AQUA releasing a song called "Barbie Girl", there had been a band called "Barbie Girl" which used the Barbie logo in all of their branding and album covers, and then tried to claim they were just a parody.