argue = argue with.
Her story is a good “plausible denial”. And if it IS what she said, it was a valid point.
If you bag is on the plane and you are not, and you know that there is not a bomb on the plane, you wave bye-bye to the bag and catch up to it later. There is no hazard in letting the bag go, because you know there is no bomb in the bag.
Trying to get your bag back by discussing the possibilities of bombs in bags with a gate agent is just abusing the TSA rules for your own convenience. You are not preventing a hazard. You are just trying to get them to turn the plane around because you want your bag, and are speculating about things that make TSA types very nervous in order to do it.
She should just get over herself and catch up with the bag later. No big deal.
Even better, she should endeavor to get to the gate on time, and the whole problem could have been avoided.