Originally Posted by
Nom
Rule book page 48 paragraph 1: "[Independent Characters] cannot, however, join vehicle squadrons (see the Vehicles section) and units that always consist of a single model (like most vehicles and monstrous creatures)." (Emphasis mine) A Carnifex brood with only one Carnifex is not a unit that always consists of a single model, thus it can be joined by an independent character.
Tyranid Codex, Page 35: "... may join a unit of Tyrant Guard exactly as if it were an independent character...". The only point the tyrant/SL uses the independent character rules is while joining the unit. The rest of the game, it is one cohesive unit. Thus, he cannot be singled out.
Also, currently, I run the unit that synack mentioned: HT w/OA Regen, LW&BS, 2+, with three Guards w/lash whips, and a prime with dual boneswords, regen, and rending claws.