I'm not ever so familiar with that history, but a quick look at the wiki suggests very much not; some of the elites were (and, at certain periods, the non-muslim population), but never the regular population, and indeed this was a major point of contention leading up to the war.

> Anyway, if we're no-true-Scotsmaning here, there also aren't any examples of dystopian colonies run by "corporations" that weren't joined at the hip with a national government.

Musk is explicitly talking about a "public-private partnership". I think any project on the scale of Mars colonization is necessarily going to be intimately entangled with one or more governments.