Flew LAX-DEN last night on a BE fare (myself and two family members) purchased with a Explorer Card. We figured we'd be nice and gate-check our carry-ons even though we'd be boarding as Group 2. I approach the GA and say we'd be happy to gate-check our carry-ons. GA asks for my name, I provide it, then she says rather loudly, "Sir, your fare doesn't include carry-on bags. You're going to have to pay for those carry-ons." I replied calmly that I used my Explorer Card to pay for the tickets so we are allowed carry-on bags. GA then typed some more, noticed her mistake and very quietly said, "My apologies." Then quickly provided bag tags.