Legal immigrants who have been here long enough to be naturalized (no oath of allegiance to the US while hanging out on a 10 year visa) and qualify for benefits is a problem in my book. Assimilate, become a citizen or GTFO!
I mentioned asylum seekers and that in some instances incurs extenuating circumstance, no problem with that. Although if they hold a green card they should be working. My wife got a green card as a "legal resident alien" on a 2 year visa with conditions (the follow-up is a 10 year visa with no conditions which can be renewed every 10 years, if you don't want to become a citizen. She knows that she has no option, I didn't bring her here to hang out on a visa. She becomes a US citizen or goes back home). Giving anyone in that group assistance of any kind is IMHO gaming the system. As I've said before, one of the conditions I had to sign to get a K1 visa for her was that I was responsible for all living and medical costs and that if I refused to provide funds for those costs she could be deported.
Just about anyone here legally can get a green card and at they point they are eligible to go out and get a job. If they can't afford their digs, cars or more kids than don't buy or have. No excuse for not working though and definitely no excuse for myself and other taxpayers to subsidize their lifestyles or burgeoning families.
I'll dig a bit more in the data though, as I don't believe that a native born child with legal immigrant parents would be considered anything but a "native born household." Not for gaming the data either, this is a serious problem (as is people who overstay their visas) and there is no room for lying to make the statistic fit your narrative.