For me it is mostly accidental, but I typically give them the rudeness when they start reading into it anyway. It's like being accused of sleeping with another woman when you did no such thing; if you have to put up with all of the crap anyway, you may as well get something out of it. So don't worry so much about whether you are being rude when you should be more worried about whether you should be wasting your time putting up with other people's nonsense.
I have one simple rule in life: everyone gets a freebie. If the sales clerk at the local Rat Shack wants to try and pimp their latest crappy phone to me then I'll give them the polite "no thanks" as I pass by. But if they are stupid enough to utter another word from that point then every person in a three block radius is going to learn some choice new ways to make someone collapse into tears solely through volume and word choice. People like to play their little hidden meaning games with us all of the time, but nothing screams, "I think that you are an idiot who doesn't know what he is saying," more than a sales puke who insists on continuing to try and sell something after being told no. I tend to apply that philosophy to everything, which is awkward the first time that someone screws it up but makes things much easier once they get it. For instance, we recently got a new guy in the department, good person and a savvy tech. A few days back he asked me, are you OK?" (It was early, I was tired, and it was work; should I be puking rainbows?) Instead of pointing out the inanity of the question, I calmly say that I'm fine and he asks, "Are you sure?" Like I was too freaking stupid to possibly understand the words that came out the first time that he asked. So he learned my rule. He still asks his intrusive questions on occasion, but never twice.
Try thinking of rudeness as a tool that you can break out whenever the situation dictates, as that's what helps me to keep the faux pleasant thing going while diverting those that set out to annoy me.