I wouldn't want to place a judgment on you or the MD based on one encounter. I've seen the nicest professionals lose their cool at times and I've seen some of the crankiest professionals do and say things that are just short of saintly. It'd be great if everyone could maintain a perfect demeanor all the time, but in all my years, I've just not ever seen that happen. There's just so much pressure working in the medical system, especially the modern medical system where the MDs are really feeling a crunch they never felt before with the insurance changes and pressure from administration. This is my experience, anyway. I'd love to say that no one will ever act out of line, but that's probably not really realistic. You'll act out of line once or twice yourself, as well, is my guess. It usually happens when your workload demand outweighs your ability to humanly perform it all and one innocent person will say or do the wrong thing and .... ugh. We all try for it to not happen, but I haven't met a person yet that it hasn't happened to.
I hope I don't sound like I'm enabling bad social behavior, I'm not. Bad social or unprofessional behavior is never good or "ok". There are reasons for it, but no "good excuses" for it, if you know what I mean. I do think, depending on the severity, it should be addressed and corrected. If it's habitual, it probably should be reported, depending on the circumstances.
I can't help but be curious why the MD was so concerned about being undermined with that particular patient. It's hard to tell from your post if there was an underlying reason for the MD's concern. Clearly he didn't handle it well, he escalated a situation that he should have known wasn't a good idea. Not only did he not communicate to you what he might have wanted to communicate to you, he undermined himself by losing his cool so publicly.
I wish I could say that I've never had an MD or another nurse or other professionals yell at me or embarrass me in front of a group, but that wouldn't be true. The truth is, I have, and more than a couple times. Most of the time it's in the heat of a moment and there's a miscommunication at the core of the issue. Sometimes it has been in a high pressure situation and it was the last thing I was worried about because our focus was on the patient. Sometimes it was someone who was misdirecting anger or frustration that I was the unlucky person to walk past. There has been a time when it was out of line, very unprofessional, and consistent and reporting it and correcting through those means was the only viable option.
I'm very glad that modern workplace culture is starting to respect and value the communication between professionals. It wasn't always like this, so this is a step in the right direction, if you ask me. At the same time, I think it's wise to keep a certain level of understanding that when humans work in high pressure situations, sometimes they do make mistakes and are less than stellar with one another, and sometimes they are just plain in the wrong. That doesn't make it right, but it also doesn't have to define a person, either.
In really high tension situations where I'm pretty sure nothing I say is going to be heard or valued at that moment and the other person is clearly triggered emotionally, I try to take deep breaths and calm myself and try to hear at least something worthwhile the person is saying. This is a skill I found very helpful with patients as well. This is probably my "type A" personality shining through, in that, if I have to be there listening to someone lose their cool at least I'm learning something from it so I don't feel like I'm wasting my time. If that doesn't work for me, I do something that I remember from the Brady Bunch. I imagine the person in their underwear as they are doing their thing, yelling at me or disrespecting me. If you ever do that method, be careful not to smirk or smile towards the person you are imagining in their underwear, they probably won't see the humor in it. At least not in that moment.
Good luck working through this one, it's never fun to be yelled at or embarrassed, I hope you find some insights from those of us who have also been through it, or maybe who have even done it.