It seems this case makes sense. You don't have a parody/1st amendment right to violate someone's trademark in a situation you can get a trademark yourself for a parody product. The song "Barbie Girl", 1st amendment protected. The parody squeeky toy is not because they are also bringing that product into the trademark arena.
Essentially, the USSC is saying, "judge if this new trademark infringes on Jack Daniel's current trademark based on trademark law." Where the question is not free expression but "are customers likely to think it's a Jack Daniel's affiliated product". The defense the USSC is telling the dog toy people to use is "no reasonable customer would think JD made or authorized these toys".
Essentially, the USSC is saying, "judge if this new trademark infringes on Jack Daniel's current trademark based on trademark law." Where the question is not free expression but "are customers likely to think it's a Jack Daniel's affiliated product". The defense the USSC is telling the dog toy people to use is "no reasonable customer would think JD made or authorized these toys".