Exactly. The methodology of the study solely involved telephone interviews to caregivers about screen time (which itself is likely to be inaccurate) and questions related to children's "well being" (also likely to be inaccurate). At no point was screen time actually measured, nor children's well-being independently assessed. The whole study is bunk.
I don't find those much more convincing. Mostly they say the negative effect comes from missing out on physical activity (in older children).
For babies, I am not sure what to think. Who watches 1 hour of movies with their baby? Were they really able to disentangle that from all other factors (socioeconomic status and so on)?