Current behavior:
After a song finishes playing, I notice that the modification date of the mp3 file has been updated to the current time and the md5sum of the file as changed. (I predict that Amarok is storing the playcount, or something similar, in the mp3 file.) I'm using Amarok 1.4.9.1.

Problem:
I listen to a lot of music. I also regularly use rsync to keep a backup drive up to date with my home directory. The above behavior is problematic because it necessitates spending a lot of time to transfer all of the songs I've listened to since the last backup.

Desired behavior:
I wish that, for whatever Amarok is doing to the mp3 file, I could Amarok to that to the database instead. That way my file system tree will remain ultra clean, and I wouldn't have to bother with so much data transfer.

Any suggestions?

Not normal behaviour for Amarok - the only time files are written to is if you modify a tag. Do you have any scripts installed that could be modifying the files? Culprits could be things that store lyrics, album art or stats to the file.