Denial can play a huge role. Perhaps the parents are hoping to God that their child one day grows out of it and, maybe, if they just ignore it, it will go away. Not everyone who HAS a SN child is ready to be a parent of a SN kid. There are soooo many kids who fly under the radar of any defined diagnosis, although there is obviously something wrong.
Tough call, OP...really. It could be that they just aren't willing to admit that their child is really that different. Or maybe they know and don't want the child to be treated differently because of any diagnosis.
For my child, no admission necessary....it's obvious. But my neighbor is in this situation where she has a diagnosis, but her child is social, has friends, gets very good grades in school, but has obsessive/compulsive quirks. She often wonders who she should tell or not tell, but doesn't want the diagnosis spread around so that event he kids know. That would just be unfair to the kid, especially if his peers were to find out the label.