That's what apple said too, but that is wrong (although I do appreciate you trying!) That checkbox is only for AUTOMATICALLY backing up ... the check box next to it is for manually backing up -- even if I backup to iCloud automatically, if I hit manually back up now, it should transfer ALL apps.
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but just for fun, I clicked this computer and tried to backup ...nothing happened. files not there
From what I understand, backing up to iTunes and copying the apps over to iTunes are not synonymous. If you back up to iTunes, that's fine, there is a backup file for your device now registered with iTunes from which you can restore your phone.
However, I believe (and someone correct me if I'm wrong) that just backing up to your computer won't sync over your apps from your phone to your iTunes App section. I think they need to be downloaded from iTunes on your computer directly to populate there. I believe the syncing would only transfer apps from your computer to your device, not the other way around. The only way they would show up in iTunes is if you A) Downloaded directly from iTunes on your computer, or B) Had automatic downloads checked so that any app you downloaded on your phone would download on iTunes on your computer.
It sounds like that may have been what was happening before, but you deleted all apps from iTunes on your computer that had automatically downloaded when they were downloaded on your phone.
That's been my experience, anyways..
