The company is in charge of itself. Everything it does alters the price.

Bought back shares strictly increase the price for existing shareholders as it takes them off the market. The entire concept is mainly due to stupidity in tax law that ends up double taxing direct dividends.

Stock buybacks are heavily regulated. They need to be tracked and publicly reported and the plans for buybacks need to be announced by the company ahead of time.

Note that buybacks must be announced beforehand by the company, so everyone selling their shares has the same knowledge.