Is this actually happening? In legal terms, what does it mean?
This is just a proxy statement, meaning it includes all proposals shareholders will be asked to vote on at Twitter's next annual meeting (on May 22nd). Everyone can submit shareholder proposals who owns at least 2000$ of stock [1]. This does not mean that anything will actually happen: The board of Twitter recommends voting AGAINST the proposal and I doubt large institutional investors will vote against the board on this, so the measure will most likely fail.
And even in the quite unlikely case the measure would be approved, it is only asking for a "report" on what selling Twitter to its users would mean. It does not argue for such a sale to actually take place.
[1]: http://theshareholderactivist.com/shareholder-activism-spotl...
My biggest issue is your last point, where owning an account would likely involve "Know Your Customer" levels of identity proving. It would likely require a new class of shares or going private, rather than buying a share on an exchange. Similarly, you'd likely only get one share no matter the number of accounts (using KYC information to de-dup, or having two notions a "member" who can have multiple "personas").
I don't know that it's a good idea for Twitter, but it's at least a (sort of) legally workable idea for an authenticated messaging platform in the abstract.
If I were starting a new Twitter, I'd consider it.
I cannot imagine the shareholders would approve this.