Error message when a file moves in the middle

[Philip Mak]

I have a nightly cronjob that uses rsync to back up the files on
another machine. Sometimes, I see error messages like this:

send_files failed to open usr/home/setsuna/Maildir/new/1010573771.27924.lina.aaanime.net: No such file or directory

It seems that the file existed at the moment rsync started, but as it
was running that file (it's a file that stores an e-mail message;
presumably the user retrieved and deleted it) was removed, so rsync
was not able to get it.

Is my assessment correct? Can I make rsync suppress this sort of error
message, so that these messages don't show up in my mailbox?