No, they are held in "street name" but the customer still owns them. You're not just a creditor of the broker. I've had a broker go bust, so I've been through the unwinding process.
A broker which just has pretend stock ownership as a book entry with the broker is called a "bucket shop".[1] A crime in most US states since the 1920s.
There may be regulatory technicalities that must be sorted out. But there isn't any reason this couldn't be handled in exactly the same way as street name shares are today. Voting rights would be interesting.
