I called the number my mom gave me and was unable to connect with an actual human being. However, the automated system clearly stated her accounts were up to date - regarding the returned book and her membership payments. So, she will be relieved to know that her conversation with the membership department on Monday was successful and she really could have ignored the collections threat.
This makes me feel SO much better. I also visited the club's Facebook page. They have over 93,000 "likes" and the only complaint posted on their page was promptly addressed. Obviously, a lot of people do like the club and are having positive experiences. And that relieves a lot of my worries about my mom's membership.
Now, I get to call my mom and take this weight off her shoulders.