I use the MCC religiously and have never once flipped a planet after building it
Yeah, I see other vetran players say this all the time. Something is up, and I don't know what it is. I still flip after I build the MCC all the time, in fact more than I want to.
I'm really quite sure that my score goes up for every planet I take by invasion, vs. flipping (Run a simple test - disable influence victory, put everything to rare on a tiny map with one enemy. If you flip all of their worlds, you still get a military victory, so you take vicotry type out as a factor for score. Now, invade the very few worlds the enemy has (usally about 3 to 5) or flip them all, both get you a military victory. Notice a difference in your score??

). Often I'm playing for score.
Because of this, if I'm playing for score, I ALWAYS leave researching the cultural line last. I try and build the MCC to prevent flipping, make sure I never build a restaurant of eternity, and if tech trading is on, I gift every last influence tech to my opponents I can.
Still, even after I build the MCC, I STILL have to worry about constantly accidentally flipping enemy worlds. I hate it. IMO, IF the MCC actually stopped enemy worlds from flipping, it would actually be even more of an advantage.
I really wish I knew what I was doing differently vs. the people that report they can't flip after the MCC. I want to shamelessly copy their playstyle so I can raise my score per world, by not ever flipping. Maybe its a bug. I wish we could figure it out.
Edit - and to be more clear, play a non MV game, and go both ways on the EXACT same map. Just save it at the outset. Then go ahead and flip the enemy. Then reload from start, play the same way, and conquer the enemy. You have eliminated almost every other variable this way.
Honestly, I wish there was an option to turn influence flipping off.