um - she's wrong.

Most libraries use the Overdrive system which will download eBooks in one of 3 formats - ePub, secure PDF, and Mobi. The nook will not handle Mobi files directly - most traditional type Romance novels are Mobi.
Drm'd ePub and secure PDF are handled by Adobe Digital editions. There is an employee of Adobe posting at mobileread.com who has been working on this project. He is not positive it will be ready to go right on Nov 30th but they will get there pretty quick. The nook will handle these file by a side load method .. ie you will download the Overdrive library books onto your computer and then plug your nook into the computer via a USB cable. The books will then be available to transfer from the computer Adobe library to the nook.
Yes, most Sony readers will also do this. Many heavy eBook users buy a "backup" Sony reader simply for the Overdrive capability. If you go to the Adobe Digital Editions FAQ you will find a list of devices which work with Adobe Digital Editions.
http://www.adobe.com/products/digitaleditions/devices/
There are ways to get all these files onto a Kindle and other devices, but it requires running some Python scripts and sometimes doing what is called "Stripping the DRM" which is technically illegal in regards to copyright law so I won't go into that here. If you are interested in that a simple Google search will teach you the method.
As for the free books, Barnes and Noble is working with the Google eBook project to make Public Domain books (out of copyright) directly available to the nook. Every single book that is digitally available in Public Domain is available for
every eReader device, either directly from one of many sites (Google, Gutenberg, manybooks etc) or via a short file conversion process.
Amazon lists many of the more popular ones directly in their store for free.
Now as for other free books, both Barnes and Noble and Amazon have self-publishing available for Indie Authors...Amazon directly on their site and Barnes and Noble via Smashwords. Many of these Authors make their books available free or very low cost. Right now, Amazon has the bigger library of Indie Authors simply because Amazon has been at this longer. I expect Barnes and Noble will eventually catch up.