Replying to myself here. I believe I have found the cause of the problem AND fixed it. We shall see.
After finding out about the 'noatime' flag on the partition, googling 'mutt noatime' immediately gave results that were much more relevant to my problem. For example, from the Mutt wiki: http://wiki.mutt.org/?MuttFaq/Folder Do a search on that page for 'noatime' and you'll find the solution right there! I had to rebuild mutt with --enable-buffy-size so that it looks at file sizes instead of atimes. It says it might give suboptimal results, so we'll see how well it goes. At the moment it seems to be working quite well; those erroneous messages about new mail are completely gone. Many thanks for your help on this, Steve. I've learned how to install CentOS SRPMS, modify the .spec file and rebuild it as a result :-) So I'm happy.