That sentence doesn't say it's the kids' fault! It's a list of things that make morning dropouts stressful: being late, kids not being co-operative, last-minute hassles with toys etc.
I don't think the parent was suggesting it's the kids' fault. In these situations, I think a lot of people go into a sort of "welp, this just can't be helped" mode, without assigning blame to anyone. The parent is saying that, if your lateness is a regular pattern, it is actually the parent's fault, and the parent should own up to it. (Occasional lateness does in general fall under the "welp, this just can't be helped" category.)
Put another way, while a parent would probably not actually assign blame for lateness to their child (though oh boy, do I know some that would...), they are nonetheless using their children as an excuse for their own bad behavior, which is rude and dishonest.
