I'm not conflating anything, but institutions like WHO and now Cornell who use this "NO EVIDENCE" construction to put people at ease on unsettled questions are relying on the fact that it
sounds like "we're experts & we say it's not happening" to laypeople, and that people don't need to do anything until there is evidence.
Re-read your source. They follow the emphasized 'NO EVIDENCE' with the phrase "there is no need to do anything". They answer many questions but finally at the bottom suggest nothing more than "owners wash their hands before and after interacting with their cats and litter boxes" - before again repeating the hypnotic, "no evidence" claim.
But as a smart person, what's your guess on whether it will ever be shown that cats can transmit Covid-19 to humans? Isn't it highly likely to be eventually demonstrated, given what we know so far? After all, how did the cat get it? If the cat tests positive, isn't it almost certainly shedding viruses? Aren't those viruses likely in the same exhaled aerosols that cause human-to-human infections? Don't many cats like to lick or nuzzle people's hands & faces?
If by basic understanding of the underlying processes, such transmission is likely – just not yet proven – is Cornell giving responsible advice? 'No evidence' is not just a "statement at a point in time" from Cornell. It's a mantra repeated six times in Cornell's FAQ, twice in all-caps for emphasis, always with the intent of putting people at ease, never paired with any analysis of the liklihood it just hasn't bee proven yet. Why don't they also say, "There's NO EVIDENCE that cats can't transmit Covid-19 to humans," which is equally true?
If you had an over-65 obese diabetic relative, with cats, and one of the cats had respiratory symptoms, and tested positive for Covid-19, would you give your relative the advice, "Cornell & the CDC say all you can do is wash your hands more"?
Or would that advice be just as fatal as WHO etc assuring people "no evidence" of human-to-human transmission existed at a date when it was WHO's primary job to know better? Or there was "no evidence" of aerosol transmission? Or "no evidence" community-masking was helpful?