Looks like the real issue is that Twitter "verified" the account. That means that Twitter is saying it's an official, Frank Sinatra twitter account. Well-known people can get verified - that's how you know you've subscribed to, say, the real William Shatner as opposed to someone falsely using Bill's name. It's my understanding that it's pretty difficult to get verified, so how this account holder got Twitter to do so is a mystery to me.
There's tons of fans of any type of celebrity imaginable who set up fan accounts. This has been embraced, to some degree at least, by the objects of said fandom, as long as the accounts are tactful.
Most famously, a fan of the show "Mad Men" set up a couple of character accounts based on show characters and started tweeting as them. She got so popular doing it, that the show - instead of suing her - hired her to run their twitter accounts and keep tweeting as those personas.
So long story short - the real issue here is with the false verification. That's a no no and Twitter should have been more on-the-ball with that.
Not now Moose, I'll tell you when.