iTunes asks to transfer purchased apps from iPhone even though app sync is off

Solution 1:

When you purchase apps (even free) on the device, iTunes always backs this up - and when it Syncs, before it does anything it backs up - and it notices that you have purchased an app/apps - so it wishes to make a backup of these apps. Click transfer and it'll all work fine - happens to me when I buy songs off of the store as well as apps