The two other terminal multiplexers I know of are GNU screen and tmux. GNU screen defines its own “screen” terminal type in terminfo, and tmux shamelessly re-uses it and claims to be “screen-256color” (screen with 256 colors). So I don’t think there is any good way to avoid it.
If I set my terminal type to something basic like vt102, and then start "tmux" and run "echo $TERM", I get "screen-256color". Also, the tmux(1) manual states:
The TERM environment variable must be set to “screen” for all programs running inside tmux. New windows will automatically have “TERM=screen” added to their environment, but care must be taken not to reset this in shell start-up files.