As long as you have a real share, and are not holding an "entitlement" (e.g. a brokerage firm holding your shares in their street name. In that case, you have the right to the economic benefits of the stock, but not the underlying. To do that your name needs to be on the company's ledger. Anyone can request to directly register their shares and hold them directly with the company's transfer agent.
I mean, unless the broker is fraudulent there’s very little practical difference; most people will go with the broker, as it tends to be cheaper. For that matter, most people aren’t investing in individual shares, they’re investing in some sort of mutual fund, so there’s another party that you have to _somewhat_ trust there.
