>>>My limited grasp of things technical had me with the assumption that broadband would need a more complete connection than a mere phone cal
I would have assumed the same until my phone line went dead (while my broadband connection functioned normally) earlier this year. It was also an exchange fault, which OpenReach fixed very quickly.
If you look at an ADSL filter
http://www.rwapservices.co.uk/images/adsladvert2.jpg
you'll see that there are only two connections to a modem/router but three to a phone.