I've run into this ID checking lady at SFO before (she works the Delta concourse), where she's demanded that I dispose of one of my two shoulder sized carry on bags before going through security.
To solve the problem, I just stuffed one of the bags into my half empty other bag.
And yep, the overstepping-her-job-requirements experience was very infuriating. She's wearing the uniform of a private security company, not TSA.