Earlier quoted context omitted.
Your registRAR's availability doesn't stop your domain from being present at the registRY, but _if_ your DNS provider becomes unavailable you'll be thankful that your registrar is able to change your NS records with the registry.
Even if you registrar's DNS you could change it in the same way. What would using different DNS acheive?
If your DNS host is unavailable _and_ they're your registrar, then you can't make changes at the registry to use a different DNS host.
But if they're unavailable and they're not your registrar, then you can still make changes at the registry to use a different DNS host (although you'll still have to deal with the two-day TTL on the NS records at the root).
So the idea of using a different registrar and DNS host amounts to separating the control and data plane for your domain.