syncthing and rsync disagree. I wonder why

What could also be the reason are how modtimes are handled by the filesystem - from the rsync man page:

–modify-window
When comparing two timestamps, rsync treats the timestamps as being equal if they differ by no more than the modify-window value. This is normally 0 (for an exact match), but you may find it useful to set this to a larger value in some situations. In particular, when transferring to or from an MS Windows FAT filesystem (which represents times with a 2-second resolution), --modify-window=1 is useful (allowing times to differ by up to 1 second).