Not quite. 54% of the 135M American workers have a retirement plan.[1] That's 73M out of the ~250M American adults. Maybe you can call that the middle class. But point taken. To be less pithy, these individual shareholders have little power to sway governance, particularly if their stock is held in a managed fund. The rich, connected shareholders steer things, and it's not always in the interests of the company in the long term.
The vast majority of Americans derive the lion’s share of their income over most of their lifetime from selling their labor, not from capital returns, whether from stock alone or any other combination of capital.
The majority of Americans own stock.