Welcome! This forum has a treasure trove of great info – Scouters helping Scouters! Just a heads up, though - all content, information, and opinions shared on this forum are those of the author, not the BSA.
The ability to see the official rosters at my.scouting.org are limited to officially-registered unit Key 3 (SM/CM, CC, COR), Key 3 Delegates designated in the Position Manager at my.scouting.org, or individuals with the Membership Inquiry functional role designated in the Position Manager. The functional positions (Key 3 Delegate & Membership Inquiry) apparently expire, although exactly when or in what circumstances is unclear to me. They can also be explicitly revoked by one of the Key 3, for example to replace one K3D with a new one.
You are the scoutmaster of the girls troop. It looks like that individual has a child in the boys troop. So, you won’t have access to see that troop roster in my.scouting, but as a committee member in the boys troop, you do have access to see that training report. As far as I can tell that individual is not registered.
You can apply for membership with the District and for MBCs it is no cost. You still have to comply with the background and YPT. The MBCs registered, as such, are in a roster accessible by the District Key 3 and the Council registrar.
Be aware that not all councils, and not all chartering organizations within councils, are OK with having someone who is a MBC counted as a scouter for the purposes of youth-protection requirements (e.g. 2-deep leadership) at unit events. I don’t personally agree with that position, but my opinion doesn’t hold sway over council or chartering organizations. Make sure your chartering org and council are OK with having a MBC serve in the unit scouter function (e.g. MC or ASM) that you’re looking at. Ideally, in my opinion, that person is registered for the role in which they are serving.