Why would anyone ask for a non-radar service from a radar controller?
I think you misunderstand NorthSouth's point. He didn't say anything about 'asking' for a service. He said they would be providing a Basic service, which is what you'll get if you're not using anything else.
As an example, if you talk to Prestwick on 119.85, you will be talking to a radar controller whatever service you are getting.
I can recall numerous occasions, notably with low level miltary a/c, when anything other than a Basic Service was declined - but I was still a radar controller being paid as such, even if the radar was u/s .......