Mozilla is even worse. If I create a new Linux distro, and include my own compiled Firefox binary, it's unlikely I would be able to call the browser "Firefox", or use the familiar fox logo, without getting permission from Mozilla. This could put me at a competitive disadvantage compared to other versions of Linux because my users would be using what appears to be unfamiliar software. It's worth mentioning that Mozilla's trademark rules also indicate they're not terribly happy about the unofficial redistribution of their binaries, either, and would prefer it if they were the exclusive source.

Is this how open source is supposed to work? Redistricted redistribution? Tight control on who can compile software and still be able to call it by its proper name?

The example I gave above has already happened. In 2004 Mozilla got a little irked at the Debian guys for distributing modified versions of Firefox (even though the modifications did not significantly change the functionality). Debian responded by mischeiveously rebranding its version of Firefox as , and a policy grew from there to rebrand all Mozilla products in a similar way: Thunderbird became Icedove, for example (which is actually a better name IMHO).

The nature of Linux and open source in general is to encourage forking and splinter projects. That's the basic freedom provided by the GNU Public License, and similar licenses. Some of the forks or splinter projects will be poor quality. Some will fail. But that's just the way things work with Linux.