Scam. Scam. Scam. Scam....
There is never - as in absolutely never ever until the sun boils and the earth burns - why an unsolicited request to access your computer from someone you don't know and haven't voluntarily asked (other than clearly genuine police and customs officials) should be anything except a scam.
No legitimate software needs it. No legitimate system you are likely to use (Mac, Windows, Linux, BSD, or anything else) ever needs or expects it. No legitimate software company (Apple, Microsoft, Google, Kaspersky, Adobe, or any other OS or software creator) ever asks or requests it. No legitimate ISP, firewall, security, networking, or landline/mobile/cable telecoms company ever phones or emails to ask for it. Nobody legitimate will ever telephone you "out of the blue" to advise that your computer has a problem or needs urgent attention due to a computer issue. No legitimate antivirus or anti-malware needs it.
The sun will die, Donald Trump will be married to Vladimir Putin, and protons will evaporate (estimated 10^34 ish years) before a request like the kind you describe is genuine and anything more than "can we persuade someone to let us access their data and install malware".
It doesn't matter what pretext or explanation they give, or how urgent it sounds - and the more jargon and urgency, the more likely that you're being called by a scammer. (Denying time to think by making it sound extremely important is a classic scammer trick)
If you want more information, it's a variant on this Microsoft service phone call scam, or this suspicious activity phone call scam, or this FTC page on tech support scams.
I don't know how to say it more directly :) But that's the bottom line.
Well done on pausing and not "diving in".