Well, if my options are to have every social gathering ruined by the immature antics of one person, I wouldn't be associating with that partner. I can see tolerating this at a casual BBQ or similar get together where there's no set agenda, but if her sole purpose is to ruin everyone else's enjoyment of a focused activity, I can't see why she has to be invited.
ETA: This is not a 'social gathering', per se; it's a gaming session with very little socializing going on. Would the opinions be the same if the game in question were, say, tennis, and Olivia kept running onto the court and blocking shots, making loud noises during serves, etc? I agree that for a casual get together partners should always be invited, but that's not the situation here.