I never remembered seeing this rule, it would be interesting, I mean its like a 6-man tag title (which could of worked well last year) but only New Day and Los Matadores would use it, for they are the only teams of 3 right now.
The Freebird Rule (named, of course, after the Fabulous Freebirds, one of the no-doubt greatest tag teams of all time) came around in the 1970's (if memory serves) and was big into the 1980's and 1990's (I'm trying to remember the last time a team used it....I'm thinking the West Texas Rednecks back in WCW?). It just says that, with a three-man team, any two can defend the belts at any time. It was actually brought about because three-man tag teams were passing away (at least as formal teams....there are, obviously, still six-man tag matches).
The NWA had a Six-Man Tag Championship (defended in six-man tag matches) that was active from 1974 to 1988 and enjoyed a brief revival in NWA 2000 in 1998.
wk