@Odysseus
Being Ring Heroes a very speculative subject, it's mostly a matter of gameplay. I mean, some heroes that are now Ring Heroes never even saw it, like Arvendui and Theoden (technically not even Saruman, even if he did want it), others had the most disgust of it (like Elrond, IF he still is a RH) other yet make even less sense like Durin and Smaug. Lore helps here, with Durin's reincarnations and Smaug's 'dragon sickness', but in the whole, they all receive the Ring from a 'what if' perspective, that is subjected to the need of having a Ring Hero available (if you want the Ring to be in the game, that is). I'm not saying it's a bad thing, but only a 'gameplay requirement' let's say.
So this would somehow 'justify' a Ring Hero Witch King, also because this version of Angmar implies that WK might not have a true will of his own, but certainly a good level of independent thought and judgement, else he wouldn't have been able to build his kingdom. That and he didn't really look for the Ring yet, as opposed to what Sauron might have preferred, or at least I think so. Let's just say Sauron worked on a good AI
But in the end, I somehow agree that the WK would immediately take the Ring back to tha boss. Well it has been suggested (and supported) that the Ring in brought to the Fortress..what happens next isn't yet fully clear, but having Sauron manifested in some way seems what could actually occur...even if technically this would go back to the vanilla game, what with Sauron re-obtaining the Ring at all. Actually, thinking about it, it wouldn't be so absurd a setting for Angmar...
On the notes:
1. Well I used to refer to them that way, my bad. Never thought much about it, sorry. About traitorious Arnorians I have no idea.
2.I did, and that's why he screamed 'Ring Hero'. Still,I think the Witch King would not react well to his betrayal, as he might have anticipated it, but he surely did not anticipate him finding the One. Treason is treason.