It certainly is "a tiny piece of the company", at an appropriate level of abstraction. Expand it out to something more specific and you get that it's "right to cast a certain number of votes in determining who is allowed to manage (act as steward of) the company's assets and other major decisions, and to some proportion of the money paid out as dividends or when the company is bought out".

Somebody who owns their own company can be thought of as equivalently having 100% of its stock.

Don't see what's "a scam" about it, but I'd love to hear your thorough analysis on the matter.