In the cases I heard of, it was nothing like that. The grandmother had not been hiding her Jewishness. The grandchildren simply didn’t realize that the fact that their mother’s mother was Jewish made them Jewish. I think the grandmother had been hidden by goyim during the holocaust and ended up intermarrying, and the kids were brought up as christians like their father. I’m not sure of the exact details (I was a kid at the time) but my impression is that it was something like that. I think there may be many cases like that, r”l.
In any case, you are right that a sheilah should be asked regarding what to say as well as whether or not the person is to be believed.