"My wallet was stolen/lost. I have no identification but I know you have all of my information in the computer. I can verify those items. I can also verify all of the information for my child if that would make you feel better. Otherwise I will have to drive home to get a passport (say name of person asking) and by the time I get back you will be closed and I will not get the medical treatment I need and may die as a result."
I go to a huge HMO and they don't bother asking any more. Their policy is ID and medical ID. Maybe because they know me. I remember when I was a lot younger I had my wisdom teeth taken out (chipped out, they grew downward) and I had my mom try to pick up my meds since I was just out of surgery, lit off my ass from the anesthesia, bleeding all over the place and kept repeating myself and not knowing I was. They wouldn't give my meds to her. By this time I felt like there was a chainsaw taken to my head and was ridiculously angry.
So I stood in line stumbling like a drunkard and leaking blood all over the place and in severe pain. It was awesome. All my blood was leaking out on the carpet. When the blood filled my mouth I let it leak out or spit it out. I let a bunch leak out all over my cheeks so I looked like a zombie.
I said give me my gosh darned pills!!! They handed them over really fast and I popped the bottle right there and swallowed a handful of crummy vicodin while cursing about being in horrific pain. It was actually funny until since I had fasted for a day I immediately drank about a gallon of orange juice that night, then barfed it out due to the acidity, tearing all the stitches. Vicodin sucks though. It didn't help at all. In fact I think I'm immune and haven't taken any liver killing painkillers for over a decade. I'm allergic to morphine so that's why I wasn't given any during the surgery. But the anesthesiologist sure was happy when I came to with his eyes pinned!
Sometimes (actually most of the time) I wish I could have lived during the nuclear family age. Seriously. I remember as a kid going to the bank and they didn't ask for ID, they knew you by name. Same with going to the doctor. There has to be places like that around still?