The most relevant point about cats being potentially invasive is not that humans feed them, but that they tend to run away from home and breed like crazy, meanwhile engaging in large-scale predation and potentially endangering the existence of local species, which would be unfamiliar with the new predator. In other words, the cats feed themselves quite expertly--just as they do in the alleyways of most cities--and don't require anything in the way of human intervention other than the original transportation. Even in places where basically nobody lives, like many of the islands of the Seychelles, cats left behind by people attempting to establish settlements have driven several local species to the brink of extinction.
(By the way, you won't find that bit of info in the article about the Seychelles, and I'm not planning to add it. I just happened to hear some scientist talking about it on the radio the other day. As such, it would take more time to reference it than I currently have at my disposal.)
I guess the obvious difference between cats and cows is that cats hunt and eat other animals, while cows just eat grass. But also relevant is the fact that cats can breed much more quickly than larger species of mammals, such as cows. So if you combine the fact that cats are predators that can produce offspring numbering in the teens each year (and by the end of the year, the first litter will be producing offspring of its own) with the fact that you can leave cats to their own devices in most places and they'll get along fine without human help, you wind up with something that has the potential to seriously disrupt the local environment.
On the other hand, if you dump a small herd of cattle in a grassy area and leave them alone, they'll breed very slowly (and also, like all ruminants, reach sexual maturity relatively slowly) and at the same time be subject to the same predators that prey on other local ruminants--which doesn't seem like an environmental catastrophe in the making so much as a temporary bonanza for the local big carnivores. At any rate, it's true that cats aren't normally an invasive species, but this is mainly because there's hardly anyplace left on earth that can support animal life where they don't already live
Cats are invasive animals!
