Yeah. It's not so much looking for loopholes, it's how to you get Bo Katan to view it as honorable and worthy of a fight. That's who you have to convince.
Back in Star Wars Rebels Season 3, Sabine Wren took the Darksaber from Darth Maul's lair on Dathomir (Maul had won it in single-combatant mortal combat in The Clone Wars Season 5 from Pre Vizsla, the leader of Death Watch and heir of the blade's creator, Tar Vizsla (and voiced by Jon Favreau to boot). Sabine had not "won" the saber, and felt extremely wrong learning to use it and resisted her mentor Kanan's push to use the blade as a symbol to reunite Mandalore behind her (even if the Mandalorian Defenders of Concord Dawn were on board with the idea). In Rebels season 4, Sabine yielded the blade over to Bo-Katan Kryze saying that Bo was the leader Mandalore needed, with the support of several Mandalorian clans.
And that's where the Mandalorian story ended, with Bo-Katan trying to reunify Mandalore under her rule. We know from The Mandalorian that this… did not go as planned. Moff Gideon got the Darksaber, Mandalore was "turned to glass" and the people shattered and divided.
I strongly believe that Bo-Katan Kryze feels that because she didn't "earn" the saber in the proper way, the story wasn't strong enough to hold Mandalore together against the might of the Empire. And to reunite Mandalore again, she'd need the actual story to do so.
Note also that Bo rejected Maul's claim to the Saber and all Mandalore at the time of The Clone Wars Season 5, saying that an outsider would never rule Mandalore. So to Bo, there are two rules here, it's gotta be a true child of Mandalore, and it's gotta be won in fair combat. I'm not sure she can accept Din's leadership either from that stance; note that she refused to accept Boba Fett as Mandalorian given that he's a clone of a foundling. She might think similarly to Minister Almec, who said that Jango Fett is no Mandalorian (he seemed to be looking down on Foundlings as not true Mandalorians, only counting those born of Mandalorian heritage with the northern-European look of fair skin/blond-or-red hair/blue-or-green eyes). She did accept Sabine's mother Ursa Wren has an ally in the Siege of Mandalore, as well as new ally Koska Reeves, both of whom have dark skin and dark hair, and were likely not born of the Mandalore core stock like she was. But perhaps she has her own rules about who is Mandalorian and who isn't… does Din count? We'll have to find out.