And if he plays cautiously and does everything right, but still loses because she's using some special ability, we get the same overall outcome without MC looking like a tool. That's why people are eyerolling at the way he lost.
There are ways to lose well and there are ways to lose while looking like a complete tool.
He literally could have won right there and then if he was going slow and cautious - like he should've been doing, given the original plan of trying to sniff out her cheating methods. But he rushes his...
So yeah, he only just noticed that his disguise is paper thin? He knew how gropey these guys were already; it's a wonder he's only had the one close call considering his cover's been entirely at the mercy of the whims of the kidnappers this whole time.