From my naive point of view, it's not clear from first principles why they must.

Investors don't run the company, they don't make product decisions on a day to day basis. They may demand growth and they may be able to fire the CEO if enough of them band together but that requires them to convince the board first (and if they can't then they may be able to fire some or even all of the board). Anyway, as long as none of that has happened I think this is an academic position at best.

I believe capitalism is defined by private ownership (not necessarily by investors) of the means of production.

Capitalism - in principle - doesn't even require that investors as such exist, much less that they own everything. That our current system has evolved into a pseudo-capitalist system which introduces all sorts of State created constructs (like corporations), and borrows elements from fascism, socialism, etc., doesn't mean that it must be this way.