It didn't actually said that she is feeding them junk food all the time.
The way I read the article, she could well be feeding them baby food in jars most of the time and some junk food more occasionally.
I had lots of extremely diet conscious friends who fed their babies food out of jars; there's nothing wrong with that. I preferred cooking because I am tight-fisted, but I doubt it was much healthier and frankly my dcs haven't been particularly healthy.
I know she said she only gives them veg once a week, but there is veg in most baby jar foods so if that is what they mainly eat then they are getting the veg, she just doesn't think about it (or was encouraged to tell her story a certain way for money).
As for the calorie list made up, surely that was the SUN extrapolating, not a dietician counting and weighing exactly what those babies were actually ingesting over a period of weeks?
If the slant put on it by the Sun is correct, then that would indeed be a disaster waiting to happen. Do we know?