Sure, any old fool can use Linux, in fact it's no easier/harder to use than Windows, but actually administering a Linux system is a totally differant thing altogeather.
Right I'm now going to counter my own argument and paradoxically back it up at the same time.
Of course Linux is easier to administer than Windows because it's easer to learn about the internals and if you have a knowledge of UNIX you're practically there. Windows is easier for most people because it does all the work for them, well infact it just pretends to and as a result most people don't have a clue so the browse under root and install any old shitware without a second thought. However Linux is harder because you have to learn about things and even with the most newb friendly distro you'll find yourself editing some text file because you've got some non-standard hardware or non-pre-packaged software.
Your nan probably can't administer either Windows or Linux. She might manage with the former for a few months but she'll probably need to call in help from someone to remove all te malware every now and again. With Linux she'd probably be hopelessly lost as soon as she buys that printer/scanner which requires her to download and compile a driver or she gets a free CD in mail which work under Linux.