That is clearly not true. What you own, is something worth X amount of Y, where Y is what other believe it is worth.
"Means of production" has a very specific meaning and what you're saying is not it.
When you buy a share in a company, you own a slice of that company. You have voting rights, access to shareholder meetings, annual reports, bod meetings etc.
What that share is worth is what others perceive it's value. what it's market "worth" is completely irrelevant to the fact you own a share.
In an increasingly large number of companies even this notion of a vote is a facade. For instance at Facebook and Google, Zuckerberg and Larry/Sergey would maintain majority control even if you bought all the stock on the open market, because of stock tiering. So when you buy stock in these companies you're practically not even buying a vote. I mean you technically are, but it's like participating in an election of with 100 other people, where one guy gets a vote that magically counts as 101 votes.
That why things like the occasional 'share holders look to force Zuckerberg out' type articles are 100% clickbait. Google and Facebook also even tried to force scenarios on shareholders where the real owners of the company were going to "sell" their shares without giving up control by introducing non-voting shares. These plans were only stopped thanks to the courts because they, of course, passed a shareholder vote. [1]
[1] - https://arstechnica.com/tech-policy/2017/09/shareholders-for...
Facebook also demonstrates it - Zuckerberg and a few others (many of whom have given him voting power on their behalf) own 'Class B' stock, which is worth 10 votes (and thus could reasonably be treated as each share being worth 10 of Class A shares). What is sold to everyone else is 'Class A' stock worth 1 vote. Despite owning fewer stock shares, then, Zuckerberg has more votes and thus has effective majority control.
You mention due to stock tiering, but that's just it, those tiers don't remove votes, or even owning a share of the company (your stock still does), it just ensures that majority control stays in the company's control. It doesn't change the claim that stock shares = shares in the company. It just changes the percentage each stock is of the company, so it's not as simple as 1 stock = 1/(# of outstanding shares) control, but it still is (100% stock) = (100% control), and (X% of voting power from stock) = (X% of control).
the stock exchanges really missed a trick by not prohibiting this sort of bullshit
When you buy a share of a company, you hold that share at a broker. That broker in turn uses a clearing company which then in turn moves shares around between accounts at DTCC on a net basis between brokers. The only company in this chain that knows what shares you own is your broker. To everyone else in the world your share is held by, for example, Fidelity or Vanguard.
You retain every economic right to the share, you just don't _technically_ own it. This gets more complicated with margin accounts, where as part of the margin agreement you agree to allow your broker to lend your shares to shorts, so for some periods of time you may not actually own the shares you think you own.
[1]: https://en.wikipedia.org/wiki/Depository_Trust_%26_Clearing_...
The obvious example being a hostile take over. One can literally buy up more of a company than anyone else and then attention to take control of the company. One defence being too literally discount shares for existing owners so they can buy up more of the company.
We just saw this happen with Twitter.