The latest iTunes 11.4 for OS X 10.6 at:
http://support.apple.com/kb/DL1774
dated: Post Date: Sep 9, 2014
has 242433227 bytes, so I assume it to be a fixed version from the 10.4 version I downloaded earlier, which had 242,940,774 bytes and did not sync my iOS devices.
I think it is either dishonest or sloppiness that the version date on the website does not get corrected, when they are fixing their oversights/mistakes. It's also odd, that when I download the current dmg, the creation date must have been left empty and gets filled by the user's download date, meaning one can't really tell when this dmg was re-created or changed by Apple. There is no change log either.
I was following the tips in this thread to successfully get rid off the error message. However my iOS devices are still not recognized. My bigger problem was that after each system shutdown/reboot, I had to re-install iTunes to get my iOS devices recognized. Apparently some sync-related iTunes 11.4 files go either missing or get changed during reboot.
The latest iTunes 11.4 for OS 10.6 has not changed this odd behavior.