I've seen a few discussions on forums/facebook etc recently, all about who should give out belt promotions.
To start, black belt is the most important promotion no doubt. So who should promote someone to black belt? Ideally it should be someone who has seen that person develop from the start of their training and given them every belt... but that can be impossible for a huge number of reasons. It should definitely be someone who has been teaching that person for at least a few years, otherwise what meaning does the belt have other than an arbitrary indicator of ability? A black belt is a sign that the instructor is happy for the student to represent them in competition and teaching at that level. An instructor who has just met someone can't know enough about a person to make that decision in good conscience.
The most official reckoning on who should promote to black belt is the IBJJF who say 2nd degree black belt and I think that's a good rule to follow. For someone to be getting promoted to black belt they should really have a direct relationship with or one step removed to a 2nd degree black belt... otherwise what sort of set-up is an academy which doesn't have a link to a 2nd degree at all?
As for belts below that, I don't think it matters too much as long as a 2nd degree is happy with it under their name or the person promoting is a black belt. What is important is that someone who regularly teaches someone and is able to judge their ability is involved in awarding the promotion. Ideally this will be a black belt, but if it's a lower belt who has been authorised to do so then so be it. The only dodgy stuff is when people promote someone to a higher or equal grade than themselves, they promote without having legitimate lineage themselves, promotion is done during a seminar outside your instructor's lineage or money has to change hands for it to happen.
Giving out and receiving a promotion should be part of an instructor-student relationship. Within that, as long as promotions are being done for honest reasons then it should be all good.