“and it’s not really our fight”
You may be technically right. Georgia has, however, been accepted for membership in NATO, just not made an official member yet.
Over the years they have worked hard making necessary political and economic reforms to meet the membership requirements and they are almost there. It would be sad to have NATO turn its back on them now and allow them to fall to the Russians on the eve of induction into the alliance. It will mean that any promise of security NATO offers is completely hallow because it seems that an attack on one is an attack on all only if it is politically convenient.
Tblisi is not worth starting WWIII over. Also consider the fact that Georgia started this by sending in an armored column into SO and fired on Russian peacekeepers.
Is anyone in the right on this one? Don't think so.