Correct, but not the whole story.
If your registrar goes down, and you have your authoritative DNS anywhere else, then literally nothing happens. They just register the domain for you and give you an interface to pass your 'glue' records up to the TLD root servers.
If those glue records point to on-site DNS, or anything that is not your registrar's DNS servers, then your registrar being down is inconsequential other than that you would not be able to update your glue records, or renew your domain.
A separate question of "what happens if my authoritative servers go down", is answered above.
The two are not one in the same, though they can be.
I actually had it running that way for a while but a couple/few/don't remember years ago Google started rejecting all the mail :-(