An update to the update!
I received a follow-up email yesterday from my son's RDO. He had obviously taken the query elsewhere after his initial reply to me, and came back with the following good news, with the reply including a direct quote from the RDO's safeguarding lead [see below] (it looks like it is applied at a national level, and seems to be a sensible approach that would fit with Viridis1886's son's recent experience):
"National FA have confirmed that referees must have a DBS in place, not in progress, to be compliant. The exception to this is referees who have reached the age of 16. The Disclosure and Barring Service will not process any applications for individuals under the age of 16. This leaves these young referees in a position where they will become non-compliant overnight, without means to prevent this. National FA have therefore confirmed they will be granted a grace period of 21 days, to enable a DBS application to be added to Online Disclosures and verified."