The stock price is mostly based on supply and demand over the short term.
Example: I buy a 10 million shares of my own stock without anyone knowing I'm going to do so, it jumps $10. Then people react and buy even more of it thinking something awesome is going on so it goes up further. I then sell a million personal shares for a huge profit. The market reacts and sells it back down to the previous level or worse, and the CEO has now extracted many millions of dollars from the company that would have otherwise stayed in the company. On top of this, they do not use that money for R&D to hire people and buy equipment, its sole purpose is to do this shell game and extract money from investors.
The description above is basically a pump and dump scheme. From general reading of business news, it appears to me that most stock buybacks ("most" in dollar terms) are not spent in this way.
Most companies do not just do a buyback once, then collapse in stock price a month or later, permanently screwing the investors. The article pointed out that Lehman did buybacks and then went broke in the financial collapse... but how many S&P 500 companies did that? Aren't the vast majority of the firms on the S&P ten years ago still in business, even though many of them did buybacks? Aren't most of them far higher now than then, despite buybacks before the crash and in recent years? Pump and dump is bad, but normal stock buybacks probably aren't.
As I understand it, the rational business case for a stock buyback depends on the company having good reason to believe that its stock is underpriced, and also having no better way to invest the cash that is spent on the buyback. Both of those conditions can occur, and if they do, all of the company's existing stockholders will benefit from the purchase.
The linked article mentions that companies that did stock buybacks were outperformed by companies that did not do them. If buybacks are being done on the up and up, meaning purely for good business reasons (not pump and dump), then arguably that is exactly what should happen. Companies with a better way to invest their money inside the company should invest internally, making the company grow. By definition, these companies have better opportunities in the first place. The buybacks didn't cause the difference, they just responded to it.
To be fair, it's possible that neither argument is correct. The small difference quoted in the article might be temporary, and would not appear if a different measurement timeframe were chosen. In other words, saying that companies which do buybacks are worse performers may not be accurate anyway in the long term. If it were accurate, investors ought to just avoid companies that do buybacks. I haven't seen consistent support for that strategy. But once it became popular, stock prices would compensate for it anyway, in which case new investors would break even.
In any case, if the companies that did the buybacks did them correctly, their shareholders all made extra profits due to the buyback decision. Remember that the company's stock was underpriced in the first place. If it wasn't, the right decision for a company that has more cash than it can invest in core business activities is to just declare a dividend. If the share price of company is low, though, buying its own stock is better than a dividend, because the future returns are higher.
You can argue that most buybacks are pump and dump actions by evil executives, not rational pro-shareholder actions by responsible executives. But you should find evidence for that. The article linked doesn't provide it.