From what I can see iTunes 12.5.1.21 might be the minimum version of iTunes required if you are going to install/restore iOS 10.0.1 to a device via iTunes. However I have just removed my current version of iTunes and installed iTunes 12.1.3.6 connected to a new empty test library. It is able to communicate with my iPhone 6+ running iOS 10.0.1. It is has just completed updating a backup set with no apparent difficulty. It also offered to transfer purchases but I didn't have time or space to let it.
It would seem that those running Windows XP or Vista may be allowed to update their devices to iOS 10.0.1 after all, provided they can do an over the air upgrade and have no need to restore using iTunes for Windows (iCloud would be OK). That said it might still be unwise to do so as there is no telling if or when Apple might make a change that breaks compatibility.
tt2