Great analysis and discussion of this very odd phenomenon.
From what I’ve experienced, it seems that the root cause of this is who they’re comparing themselves to. Wealthy people tend to compare themselves to wealthy people. So, if they have a few million but they can’t manage to fly first class or take four-month vacations, they must be middle class.
This became especially noticeable when I attended graduate school. The (objectively wealthy) Philosophy professors I rubbed shoulders with would often comment that they don’t make much money or slot themselves in the middle class. And the reason is that they compared themselves to their higher-earning peers in the med school, not the grad students who littered their halls or the custodial staff that kept their offices and common spaces clean.