That's the standard interpretation of the Four Freedoms. Unfortunately, I think it ignores that most users can't code. The Four Freedoms, practically, protect developers and the freedom to hack. These are good things to protect, but it's not the same as protecting the interests of users.
It can be argued that GPL'd code (in contrast to a license such as BSD) is less a net positive for users because the constraints the GPL places on how code may be used (requiring any user to expose modifications made to the GPL'd code along with a subset of the code connected to the modified code) means that some developers may not choose to use that code in their application. This results in fewer applications, which means fewer ways for users to solve their problems.
For Carmack in particular, I think that's the argument he's making. Carmack's goal isn't to guarantee developers maximum freedom to hack; his goal is to get his code in as many places as possible (because he prides himself on being the smartest guy in the room, and the more people use his code the more proof there is of that assertion). Maximal code adoption is not served by a GPL license; the GPL license sacrifices a bit of that opportunity to protect the developers' freedom to hack.
It can be argued that GPL'd code (in contrast to a license such as BSD) is less a net positive for users because the constraints the GPL places on how code may be used (requiring any user to expose modifications made to the GPL'd code along with a subset of the code connected to the modified code) means that some developers may not choose to use that code in their application. This results in fewer applications, which means fewer ways for users to solve their problems.
For Carmack in particular, I think that's the argument he's making. Carmack's goal isn't to guarantee developers maximum freedom to hack; his goal is to get his code in as many places as possible (because he prides himself on being the smartest guy in the room, and the more people use his code the more proof there is of that assertion). Maximal code adoption is not served by a GPL license; the GPL license sacrifices a bit of that opportunity to protect the developers' freedom to hack.