Curious. On 1 website, WP 3.5 (not upgraded, German WP install), the problem persisted for 5 days after the monthly full backup was initially scheduled. From Jan 19th 2013 till Jan 23rd 2013, then it stopped.
Because of an update I am about to implement, I have to run a manual full backup now, but I will keep monitoring it's behavior to see whether the problem of daily backups returns or not.
I have also setup a clean installation of WP 3.5.1 (opposed to the earlier tested WP 3.5.1 installation which was upgraded from WP 3.5 to 3.5.1) with BackUpWordPress 2.1.3 running on it, with currently no manual schedule configured to see what happens and what happens after I set one up after a few days.
The same test-setup for WP 3.4.2 and 3.4.1.