I think this is one of those things that one wants to believe, but there just isn't enough definitive science on the subject. I didn't see the 20/20 episode but I read the magazine article about the nursing home cat that visited residents hours before their deaths.
There's some compelling theory, especially about the "smell of death" that we can't detect but that cats likely can. I should think that dogs would be able to detect the same odors.
It just seems to me that, since cats are common nursing home residents all across the country, that if it were true, we'd hear many more similar reports.
We'd probably also hear about a sudden rash of mysterious nursing home cat disappearances.