I'm with LR. I personally don't date people without meeting their other partners. It's not so much to make sure they're telling the truth. I like to think I'm a fairly good judge of character. I just need to know if anyone in my sphere is a psycho and if I should get the fuck out before it's too late.
Plus, I've found it's not uncommon for metamours to be good friends. Not always of course, everyone's different... but if you're both in to the same guy, there's a pretty good chance you have some things in common.
And it always helps to meet people so you see each other as a real person, not some ephemeral object of competition. If things get serious, you will eventually need to talk personally about issues that come up, not going through Falcon. No matter how good someone might be at communication, nobody is perfect at the Telephone Game, which relies on reinterpreting someone else's interpretation. If there's confusion, he would be guessing at the clarification. If you speak with her directly, she can ask you "Is this what you mean?" and you can clarify.
Labels are sticky and I hate the glue they leave behind.