IOS updates and upgrades can go wrong for any number of reasons. I am really glad that a fresh restore worked in your case, however, there is NO rule which says it must be on a "Primary Authorised Computer" to work. What you experienced was simply a bad upgrade which could happen for ANY reason.
The restore process is EXACTLY the same on any PC with iTunes. That is why, for example, any Apple employee could restore your device for you in an Apple store. It is also the reason I can help my friends by doing it for them on my PC. That would be impossible if success was tied to one "master" PC per device, wouldn't it?
I am very glad you go it sorted though. I just want to make that clear so that our members do not misunderstand and believe they can only successfully restore on one "primary" PC. That is no how Apple devices work.
The only thing you are tied to is synchronizing your iTunes library from one PC. Devices can be restored on any PC.