There was a statement made by Microsoft about being 300 miles or more from home. Different ISP makes more sense but I suppose you could be connecting with the same ISP and be far away. And yes the solutions are insane. I emailed Microsoft about this and got a reply which was a canned list of how to get a trusted device, etc. which wasn't helpful. The Authenticator app I downloaded from the app store I set up and it gives me a numerical code to use but I don't know where I will be using it.
I used to travel with my laptop and went through the process of setting it up also with the help of Microsoft and it works but I am not traveling with my laptop now. One other solution is to use Gmail. I set up Gmail on my PC and linked it to Outlook.com such that any messages sent to Outlook are also sent to Gmail. Now I will have to see if I can make that happen on my IPAD. Verifying a device should be a simple procedure but Microsoft has made it a rube goldberg process.