So Connie was in no position to refuse the inquest apart from legal grounds, which she had limited protection on thanks to Randy, but she decided to come because Debbie was the host of the last Doe Masque, meaning she'd probably have leads regarding Scarlet's death. She decided to take the gamble, saving her outward social standing (by not refusing one of the Big Four) and seeking to potentially win information over. I can follow the reasoning.
Her mistake, however, was thinking that Debbie's lackeys were like the bystanders during the Pamela affair, who would sway under sufficient pressure—she did not take into account how Debbie flings her weight around since, objectively, she did hold the most power in the room.
On one hand, it was cool that she and Scarlet learned to work together in mutual trust for once, and that the switch was not Scarlet saving Connie, but Connie actively pushing back. In the other hand, not only did she fail the gamble (for info), it could've gone more disastrously had Randy not ask for help.
Bit of an asspull, but I think Connie is progressing in the right direction as an MC. Her mindset has formed enough of an ego that she did not want to take people trampling on her sitting down. She simply needs more resourcefulness, which she severely lacks so far.