Steve, I agree my example may not have been totally clear. Yes, a Basic Service can be offered by a LARS service. But a Basic Service can also be offered by someone without a radar feed. For example,
AFAIK, London Info doesn't (formally) have radar available.
(Rumour has it that London Info does have access to radar, but either the radar feed or the controllers are not certified, so they cannot use it to offer e.g. a Traffic Service. But it does help them in identifying aircraft positions.)