They do, and it is mostly fraud.
The most common way of self-promotion is founding a "new" martial art (or governing body) and claim to be e.g. 10th dan in that martial art or governing body respectively.
Most of these guys do gather people who have no idea about martial arts around them and promote their nonsense as secret art or whatever. If they are called out and not stupid enough to believe their own delusions, they simply avoid any confrontation with valid fighters. See Frank Dux.
Another possibility is that this happens due to politics, i.e. like you suggest, some teacher (or federation) is not promoting due to personal or political reasons and at some point, people start promoting themselves. I think that this is equally invalid in most cases. There is the possibility to change affiliations and get an orderly promotion by higher ranks.
Additionally, as many high-ranked judokas in Germany hold, the belt is there to hold the gi; one should never put too much importance on rank, really. So even if there is only one unified governing body available and one has the feeling a promotion or the possibility to do higher grades were due, one should simply not think in terms of "deserving" a higher rank. This whole mindset of having one stripe more or less on one's belt being of importance is problematic in and of itself.
There is at least one notable exception, though:
Ben Askren, a horrific wrestler and prolific wrestling coach, declared himself a BJJ black belt without ever having held a rank in BJJ. He challenged anyone who dared to question this rank to take the belt from him by beating him in a match. Nobody did. That highlights the same point as the last paragraph: Does the fact that nobody would ever have awarded this grade to Ben Askren really mean anything? Not really, it is all about skill. So what he did was to ridicule the whole system of BJJ (especially based on training methodology) by pointing out that through his methodology, he got more proficient in everything that is important for a BJJ black belt than (most) BJJ black belts. Since this belt is not awarded by a higher rank, it is not worth anything formally, still. It is a statement, nothing more.
In the end, it does not really matter which rank one holds according to whom. My first Judo teacher was a 4th dan according to the official governing body and was as proud as one can be as he was awarded 5th dan by the older (Budo) organisation of all budo black belts. It was not officially acknowledged, but it was mere politics that he was withheld the official promotion and everyone knew he deserved it. But still, he would never have promoted himself. After all, there hadn't been a rank system until quite recently (~150 years) compared to the history of systemized martial arts training (probably thousands of years), after all. What matters is one's ability as a martial artist and an instructor.