I think someone is more likely to remember who they lent something to that they never got back, than the borrower who forgot to give it back.
Maybe your friend insisted on lending it to you as they thought you’d enjoy it, you looked at it and didn’t think it was something you’d usually read but took it out of politeness fully intending to read at some point. You put it down somewhere, then ended up forgetting about it. You never read it, hence having no memory of it.
I have been stung by friends not returning lent stuff. One set of friends we lent a tv series boxset of DVD’s and 2 camp beds when they had some friends coming to stay and they didn’t have a bed for them. It was my husband that lent them the dvd set (it was mine of one of my favourite series) and I was cross with him because they’d never given back the camp beds and when we reminded them they said they didn’t have them so must have given them back already. So I asked about the DVD’s… they said they didn’t have them and asked if maybe we’d lent it to someone else after them. I ended up buying a replacement set. I would cat sit for them and one time I spotted the set on their shelf so I mentioned it again - they said it was their copy. Years later, they came to ours for a party and had the dvd boxset on hand… said they’d found it and thought it was ours. A couple of years after that, I spotted them selling a pair of camp beds on FB marketplace. I couldn’t be 100% certain, but was fairly sure they were the ones we had lent them that they were adamant they’d given back at the time.
A few days before the WFH announcement during Covid, I did a mental health first aider course at work. I got some books with it and one was a guide for line managers - I wasn’t a line manager, but it would be useful if I needed to provide guidance to a LM. My own LM at the time was interested in the course etc and when she saw the book asked me if she could borrow it. No problem. Then of course the WFH order came in and it obviously went on for longer than people were expecting. I must admit I forgot about the book at the time because work was crazily busy and I was working 60-80 hour weeks. My LM left the business around a year later. A meet up was arranged with her and a few who could make it from our team to see her and say goodbye. I couldn’t make it, so I text her and asked if she could give the book to one of the others as there were 2 of them that I was close with and would be seeing out of work. She replied to say she couldn’t find it…
I had an online group of mum friends from Babycentre who all had babies due around the same time. I had a USB stick with around 500 books on it for a kindle. We all exchanged addresses and everyone wanted to borrow it to copy the files for themselves, so we agreed I’d send to the first person, they’d send to the next and so on til everyone had had it and then return to me. It was working really well - 8 people had received it and copied the files and then the second to last person never received it (or possibly received it and lied I guess).
So in my experience, if you are someone who lends things to people, you often end up losing things because of CF’s in your life. And you do remember exactly who you lent what to and who kept it. The fact you say it’s a possibility she did lend it to you tells me you know you’re the sort that borrows stuff and doesn’t always remember to give it back. It might not be intentional, but if you know it happens, it’s far more likely your friend is remembering correctly.
Do you think there might be other things this friend lent you over the years that you haven’t given back and your friend is just fed up and has only mentioned the book as a single example? If you value the friendship, get her a copy of the book, give it to her and tell her you’re really sorry, you forgot you’d ever had it. And never borrow anything from her again (and don’t ask to borrow stuff).
Sorry that was so long! I have other examples too - I no longer lend to anyone.