The most valuable rule of any new job - keep your mouth shut for the first 2 weeks and learn everything you can about anything that pertains to a company and its workers.
I don't know what happened in this situation, but I find it somewhat implausible that you were fired on the basis of them being threatened or feelings being hurt - you basically came in as a nobody (interns aren't actually nobodies, but c'mon, you're new on the bottom rung) and threw your weight around. That's a red flag for a company that has to invest in you. Free or not, they're investing time and energy into accomodating you and giving you a space to learn, and you throw it in their face rather than take the opportunity to see how others established do their work.
"Surge of gratitude and magnanimous energy" reads to me like "I rolled up my sleeves and showed these bozos what's up". It's totally the wrong attitude.
You did create a hostile work environment by doing what you did in this fashion - if I was an established designer in a company, I would have little patience for an intern who thinks they are the shit on Day 1. If you are that good, apply for a lead role. Otherwise, take a serious hard think about how you can approach your next role with a beginner's mind. Good luck!