It means the stock broker owns the Tesla shares. On the broker's record books, the Tesla shares are custodised for that Tesla investor. The shareholder records of Tesla, Inc. would not record the name of that Tesla investor unless that Tesla investor holds Tesla shares directly by some other means.
This is the normal way.
Of course, Tesla could try to access the records of every stock broker in the world to check who is the real owner of the Tesla shares. Not sure how Tesla would be able to do that. And if the stock brokers would allow Tesla to access their records.
The best is to tweet Elon Musk to find out how to own Tesla shares to access IPO for SpaceX.