It's a little different than that. Verizon had a deal with Yahoo that allowed Verizon users to keep their "@verizon.net" email addresses but use Yahoo's email servers. You could log into Yahoo with "user@verizon.net" and get your verizon.net email through Yahoo's webmail interface. In fact, logging into Verizon's portal just redirects to Yahoo. In addition, your POP server was "incoming.yahoo.verizon.net" instead of the normal Verizon server. Fairpoint is not continuing this deal with Yahoo so now to access your new "@myfairpoint.net" email through a web browser you'll have to go to Fairpoint's web portal instead of Yahoo's and have to use Fairpoint's POP servers. If you have an "@yahoo.com" email address nothing is changing as far as I can tell.

Yeah, that might work in a controlled environment. However, doing this in the home environment gets very difficult to the point of being unworkable it seems. It gets particularly tricky if the vulnerable service is in some piece of the networking stack, which in Windows probably includes IE.