That is not the point GP was making. The assistant you mention is still paid by the municipality, so they show up in GDP numbers just as much as if you paid them yourself.

What doesn't show up in GDP numbers are cultures where people take their elderly relatives into their own homes and care for them themselves. Same as hiring someone to look after your kids, or taking them to day care, shows up in GDP; while having their grandparents or other family care for the kids while you're off to work does not.