I agree with your ideas. That 2 bond N is a typo, it should have an H (that it got from that alkane). And since there is preference for the tertiary spot, I would expect this to be a triplet (radical) nitrene mechanism. The singlet doesn't have much preference for primary, secondary etc that I know of since its a direct insertion.
In real life this would be a pretty messy reaction since nitrenes can undergo intrasystem crossing and give both singlet and triplet products, and neither is that picky about what it attacks.