I don't mean to suggest that "I'm a dum dum" is a bad approach - in fact I think it's great for getting past any cynical defenses that have built up.
But I'll never forget taking my son to the ER and getting to have an actual conversation with a doc. When he was a toddler he would get nasty respiratory infections that had escalated to hospitalizations in the past. When I took him in, he was in reasonably good shape, and initially the doctor just wanted to send us home. But I described his history and said something like "every time he has one of these, we wind up taking him back into the ER at night, where they invariably give him a steroid that clears him right up. Could you just prescribe it to him now, and we'll only use it if it becomes necessary?"
The doc got this big smile and was more than happy to oblige. My guess is that she didn't want to prescribe a steroid for no reason (because they really shouldn't be taken willy nilly), but as soon as I showed her I was, you know, thoughtful and responsible, she was practically falling over herself to help me.
Docs don't want you having to bring your kids to the ER at midnight any more than you do. And for the most part they're in the field for good reasons (especially pediatrics, because you'd have to be insane to do it for the wrong reasons).