No, you cannot discount the 0, in Italians phone numbers is used even if calling from outside the country.
Trust the Italians to be difficult and insist on going against the trend...
06 is Rome region.
I guess assuming your first statement is true, then yes I guess if we look at it in E.164 form "italy style".... 3906 is indeed Rome... however 396 is reserved for future usage. Sort of a good example as to why most sane countries drop the trunk prefix (0) in E.164 for the sake of clarity and avoidance of confusion !
(or in the case of the American cousins, don't use 0 in their trunks in the first place)