If the wifi provider is hijacking DNS and returning "helpful" responses when your laptop looks up something that a public server can't resolve, instead of the proper NXDOMAIN response, they're pointed at the web server that is supposed to return an advert-laden suggestion of what your typo-ed URL might have been. Obviously that web server can't respond to a login request, but because the DNS lookup didn't fail, the client can be fooled into thinking it's on the home network and the domain controller is down, with predictably hilarious results.
So it might be neither Microsoft nor your IT department, but beardy train man's WiFi breaking the rules that's causing the problem