One of my few talents is that I'm really good dealing with bureaucracies. Not in the long run, where they drive me crazy, but in the short run, when they're telling you that you should buy the ticket and they'll refund it, or that you have to pay your entire year's out-of-pocket expense and then apply for a reimbursement. In situations like that, I go into debugging mode: persistent but not angry. My favorite line is when I'm talking to the person and I say "I know and you know that you can either help me or escalate the problem to someone who can help. And I'm going to keep talking to you until one of those two things happen." Yeah, I know it's kind of obnoxious, but I think they appreciate that I'm not emotional about it -- I'm persistent and I maintain eye contact but I know it's not a person denying me fairness, it's a program.
Or when they answer your question with a specific not-quite-relevant phrase and you say "Ah hah! That's a script constant! That points the way to the sub-routine!" For instance, I was recently talking to a hospital financial person and she kept saying "What we're dealing with is estimated charges," and I realized "Oh! She's forbidden from saying 'you aren't responsible for 30% of this, you're responsible for 30% of the adjusted charges. So all of this is just a Kabuki dance to get the hospital as much money as possible, to guard against deadbeats and, possibly, to float an interest-free loan from people who aren't programmers." And three minutes later we were both all smiles and laughing with our shared, but unspoken, understanding of the situation.