I think it's a "best effort" matchmaking, so you're not guaranteed to match a team with an identical card. Here are my datapoints:

My first Lighthouse trip I had the only 8-0 card in my fireteam. The other two had newer cards with a loss or two on them. When we lost that match and I blew my mercy, I saw that one of our opponents hit the lighthouse, implying that we were playing a team that also only had one 8-0 member.

My second card was synced with my fireteam, and we were paying very close attention to our opponents before each match. We were playing teams in lockstep with our cards. We lost to a 7-0 team when we were 7-0 to blow mercy, and we beat an 8-0 team for the Lighthouse.

There might be an interesting "strategy" buried in there for getting single fireteam members to the lighthouse, where you all blow through the first five games or so, then have two members leave, reset their cards, and throw a couple games. You then join back up with your 5-0 teammate and proceed to drag the matchmaking down.