Given that identity fraud leads directly into what is functionally actual theft (taking money out of you bank account or taking up loans in your name and scarpering), there's no wonder the term's confused. Doesn't make it theft though.
It isn't legally theft, but because people commonly use the word that way, it is colloquially theft. The qualifications are different. Legal crimes are defined by law. English is defined by its common use. They're not necessarily the same thing.
Just as many wiki's are called Wikipedias, by analogy with the biggest ones; that is, they aren't. Or maybe more fitting here, the word 'download', which can mean data transfer or modification in pretty much any way with a person not knowledgeable about computers.[1] Those uses aren't uncommon, but they are nevertheless wrong.
I think you just finished a circle there, so I don't think there's much reason to continue this line of enquiry, given neither of us is going to change our stance.
No, colloquial English doesn't require this. e.g. "Identity theft"