Since the files were so large and I didn’t want to wait to re-upload them, I found out that another plug-in I was using (WordPress Media Library Folders) also had a sync option on a per-folder basis, so I was able to sync the files in each of the folders that Media Sync had an error for. It worked just fine with no issues.
Also, I don’t think I have any database issues because everything else seems to be functioning fine. I also have no idea what a multisite WordPress installation is, but I’d guess mine is not.
Not sure I understand the resolution that was given here, but I seem to be having the same issue. With some of the files (most of them sync just fine), all of which are .mp3 files so far, I get the error
Attach ID not received for inserted attachment (wp_posts table) for file:…
just the same as op. If there is a way to fix this issue, that information would be greatly appreciated.