My boss had an online meeting today - and of course this presenter wanted to use Skype, plain ol' Skype, not Skype for Business.
Skype for Business is installed on Windows 10 by default (which I have not removed) but seemingly, Skype for Business will only allow logons from MS business accounts (which I suppose makes sense).
So - my boss couldn't do her meeting because she was missing the needed software.
So let's get back to the original issue...
Only the boss can determine what software she is going to allow. Nothing that she says, requires, demands, etc. matter, because she's the boss and her actual decision is what goes. Period. No amount of IT banter in this forum can change that, it's fact. Your only way to change this, is to get her removed. So if "do what is needed, instead of what is said" is done, then obviously the correct action is to get her fired. That's not going to happen, so let's not talk like that's an option. She's the boss, she makes the rules, and using these products are her decision, end of story.
Skype for Business isn't a factor here.
Your boss could do her meeting. That she didn't is, again, all on her. Yes, you can help here if she tells you what she has decided to use and asks you how to use it. But she wasn't missing software, she just didn't know how to use a product she agreed to use and presumably didn't ask for help early enough on it.
In this one case, the fix is training the head of IT how to use a web based Skype interface. That's easy if she is okay with that. This assumes many things, though, as it seems that many of the problems come from the boss being capricious and illogical. So any given fix may or may not make her happy, we can't tell.
In other cases, there is no universal answer. We fix this by not allowing other companies to dictate our software stack. Things like Skype are allowed specifically because they work in any browser. But things like Webex are not because... we simply don't have the infrastructure to make them work and it is on the vendor to provide viable systems.
At the end of the day, she is the boss and her actions not her words are her actual rules. Words that conflict with actions aren't your mandate, they cannot be.