I am not sure I am quite as keen to criticise the lounge visit, I am not clear why everyone doing that is ignoring the OP's report.

The lounge is closer to connections security than the gate, and yet when they arrived at the lounge they were already offloaded. Had they gone to the gate it would have taken longer and they wouldn't have been any less offloaded. It's possible had they been at the gate they could have been put back on, but based on the report the gate staff wouldn't do it anyway.