I've been a typical IT person for a very long time. In the last few years, I got into contact with salespeople, by being basically a sales engineer.
And I've learned that there is a reason to make a call besides the publicity aspect: A call (and I mean call with voice and possibly video) forces immediacy. It puts both parties on the spot. Or rather just the party being called, because hopefully the caller did prepare for the call. Also, this immediacy enables rash and uninformed decisions, whereas asynchronous communications enable more deliberation and research. In sales, you don't want deliberation. You want to get this over quick and easy. And if you've dealt with a long long email chain that goes back and forth quibbling over minutiae, a call can reduce this kind of indecisiveness and inhibition.
So I see this whole thing as insulting in even more ways: A "quick" call means that it is an unprepared one. Also emphasized by the lack of real topic or agenda beyond what the original post already stated. No way forward for the other party that is possible to prepare for. No prior chain of communications, so if the call is really the first reaction in the first short email, this means "you are unimportant, I don't want to waste time, let's get this over with".
Also, in many cultures (I've only had to deal with European ones, so no idea if this really applies to the rest of the world), setting a stage is important. There is a cultural meaning to CC-ing a manager, to inviting more people than necessary to a meeting, or to do things publically or in private. A bigger stage formalizes things, gives importance, emphasizes seriousness. A smaller, private stage can mean the opposite: you might want the other party so safe face, because what you are going to tell more informally them is that they fucked up. You might want to get them to agree to something they could not easily agree to in public. Announcing publically, that there should be a private meeting is the worst of all kinds: Basically, this signals to the public that this person fucked up and is getting scolded, more serious than a totally private scolding, less serious than a totally public one. Why else would you widely announce a private meeting invite?
I don't know if the resignation in the original article is really a final resignation or rather some kind of cultural signal. I've seen that kind of drama used as means to an end, just think of the stereotypical italian lovers' discussion where both are short of throwing each other off the balcony, just to get very friendly a minute later. But in any case, whether it is deliberate drama or a genuine resignation, the necessary reaction has to be similar: You need to treat it as if it were a real resignation publically and respond with all the usual platitudes that they are very valuable, you are so sorry to see them go and you'd do almost anything to keep them. Then you privately meet in private and find out which one it is, and maybe fix things. It is a dance, and you have to do the right steps. If you don't know the right ones, at least think hard (you have the time, it is email) on how not to step on any toes. The Mozilla people failed in that...