Take in mind that private interactions not only do not offer many hooks for other people to jump in, but they also don't offer many hooks for people to include other characters. The "closed-off-ness", as long as it's in-character, is then a reasonable consequence of the nature of the interaction. You wouldn't invite a random stranger when you are discussing personal matters, after all (unless you were really, really outgoing).
This is, of course, if the 'brush off' is strictly in-character. Ignoring or telling someone to go away OOCly when you are roleplaying in the open isn't acceptable: if you don't want to get interrupted, use party chat. The least you can do when roleplaying in /say is to acknowledge interruptions IC-ly. Then you can be as rude as your character allows you to be.
This is, of course, if the 'brush off' is strictly in-character. Ignoring or telling someone to go away OOCly when you are roleplaying in the open isn't acceptable: if you don't want to get interrupted, use party chat. The least you can do when roleplaying in /say is to acknowledge interruptions IC-ly. Then you can be as rude as your character allows you to be.