This is of course true of every other terminal emulator as well, and indeed it's not only colours that are incorrect. Function and editing keys get recognized incorrectly; REP can get used where it does not work; and even simple relative cursor motions can be done wrongly.
TERM and the ideas incorporated into terminfo/termcap are inherent in the way that terminal devices work on Unices and Linux-based operating systems. That there are different terminals and terminal emulators not all speaking exactly the same protocol is also an unavoidable reality.
Setting TERM properly isn't some tmux-specific problem.