nrb80, if it were your child who might not get into the school because someone was scamming their kids in, how would you feel?
Exactly the same. I also provide free legal services and other volunteer hours to low income families in my incredibly wealthy county - including assisting with representations of children who are being bounced from schools due to accusations of false homelessness or similar.
Regardless, how I would feel, or you would feel, or the OP would feel isn't really the point. As to the OP's original question, I would not accuse a person of falsifying their residence based only on neighborhood gossip or what the person said to me socially. If the person said "I really live in Connecticut, and I am never in New Jersey, and I know I have no right to send my kids to New Jersey schools, but I love this school so I am going to scam my way in" I would probably say something. As to my point, I don't think it is polite or effective to repeat gossip and conjecture - and moreover, the school system has their own verification methods. In our school system, accusations like this are usually either ignored - to some extent, if a person issues a false lease to an adult child and moves the utilities to the adult child's name and so on, there's nothing that can be done - or are now sent to a referral for assistance and services - to help families who are trying to keep their kids in their old school now that they are homeless or casually homed.
There are a couple of chronic complainers that apparently exist - and their complaints reflect badly on them, not on those they complain about. Here, the issue is complaints about multi-generational families living in houses, and whether a child "really" lives at the house or is just visiting.
Which is a long way of saying that the social wheels are greased by kindness and dignity. And it there is such an incredible issue in the OP's community then the way of dealing with it is through the school board and/or other appropriate citizen-facing body - advocating for different verification procedures, etc, rather than repeating gossip and conjecture about one family.