I'm going to assume this applies to most shops that have a 撮影 option, but I've asked the girls at three different shops (Cocodoll, E+ Shinagawa, and one more I'm forgetting) and all have told me that the recording option requires you to provide your passport for the shop to make a copy of and for you to sign an agreement that you won't upload the video anywhere online. I wouldn't recommend this, so I've refrained from the option whenever I get the same answer.
Maybe there are shops that are lax on this, and would love to hear if so. Also interested to know if anyone has gone through with providing their passport and signing the agreement