Well, technically the name of the gender is "not masculine-personal". It can be treated as a kind of exception in a way = children can for sure include some boys, but as the word itself is neuter it's not masculine-personal anyway.
And for not masculine-personal plural, Accusative is the same as Nominative. I'd treat the fact that Genitive is also identical to them here, simply as an accident ;)
I've seen several examples of this in this course and I've always wondered why one way is accepted and one isn't. In my opinion there might be slightly more emphasis when you include any, but the sentences still mean the exact same thing.
The only way I can think of that it would matter would be something like: "Your uncle has two children, right?" "No, my uncle doesn't have any children". Is the Polish emphasis something similar?