Just came across this thread, which supports what I discovered after posting the following:
https://discussions.apple.com/thread/5331886?answerId=23064036022#23064036022
The morning iOS 7 was released, I had connected my iPhone 4 to my MacBook Pro to back-up and charge. At the time I was running iTunes 10.7. 'Other' on my phone was reading .85GB. At this point there was no badge on Settings indicating iOS 7 was available. Like Cravit 8, I've always had the boxes that have anything to do with "software" and "automatically" unchecked.
Yesterday, I updated my MacBook Pro to iTunes 11.1, and made sure the boxes were still unchecked, as I don't want iOS 7 on my phone given all the issues that have been reported, not to mention the fact that the UI is ugly. I then connected my iPhone again, and noticed that 'Other' had jumped to 2.85 GB. As I had only used the phone to make several calls and play Sudoku, the jump was a bit alarming. At this point there was still no red badge on Settings. After spending some time searching the internet for info on the matter, I went into Settings > General > Software Update, and discovered my phone was downloading iOS 7.
That said, the ONLY time I go into 'Settings' is at the end of the month to 'Reset Statistics' of my 'Cellular Usage'.
Having discovered the reason for the jump in 'Other', I decided to set-up the phone as new, adjust all my settings, reinstall my Apps/Music and create a new back-up, after which 'Other' was down to .45 GB. An hour of so later, I noticed the red badge on 'Settings', and sure enough my phone had automatically downloaded iOS 7 again without ever having gone into 'Software Update'.
Last night I set-up the phone as new a 2nd time, and upon waking up this morning found the phone had again downloaded iOS 7, without ever having gone into 'Software Update'. 'Other' now has jumped from the .45 GB after setting up the phone as new, to 2.58 GB.
Of the three iPhones I've set up for friends, two have had the exact same thing occur, and like me they never went into 'Software Update'. Fortunately, I have a 32GB iPhone, so even with my Apps and Music installed I still have 11GB available.
So to Kilted Tim, stevejobfan0123, sberman et al., your wrong!!! Given my experience, I have to agree with Cravit8 that "there is a setting or matrix of settings in iTunes causing the download to be pushed to the device (or automatically downloaded)".