This completely ignores the main data point presented in the article; namely, that those things are more cute than babies, which seems to need explaining.

Needs explaining, yes. But personally, I would give evo-psych a chance to attempt an explanation before I decided that we need caution about the entire field.

1. Some people find babies cuter.
2. There is cultural conditioning to consider animals cute (e.g. Disney).
3. Superstimuli can exist in nature; see knb's example about eggs. Furthermore, EEA humans spend way more time close-up around human babies than around babies of any other species.
4. Our common ancestor with other mammals perhaps found its young cute. This could explain why some people find furriness to be cute: the babies of our ancestors were furry. The association between furriness and cuteness might linger in our psychology, because there was no reason for it go away. Our notions of baby-cuteness may have evolutionary baggage that makes it less-then-precisely targeted at human babies; there just wasn't a need for natural selection to clean that baggage out.

There may not have been any danger of humans in the EEA taking care of cute animals in a way that hurt their reproductive success. If humans happened to evolve a notion of cuteness that (in at least some humans) was activated more strongly by other mammalian young (due to a common ancestor, or accident), there might not have been selection against it if that superstimulus didn't hurt human reproductive success.