This is the story people tell in business schools and economics departments, but there's more to it than that.
It's also a way to sterilize new issuance to employees, primarily senior management. In a very real sense, it can be a backdoor payment to management. Issue shares to management. Buy shares on the market. Net effect is cash to management.
If buybacks are funded by debt issuance, it's also a way to lever the company. Remember Apple and Carl Icahn? That particular episode looks a lot like greenmail. Apple bought back shares, mainly from Icahn, so that Icahn would go away. The buybacks weren't exclusively from Icahn, so it wasn't technically greenmail.
It's also a way to sterilize new issuance to employees, primarily senior management. In a very real sense, it can be a backdoor payment to management. Issue shares to management. Buy shares on the market. Net effect is cash to management.
If buybacks are funded by debt issuance, it's also a way to lever the company. Remember Apple and Carl Icahn? That particular episode looks a lot like greenmail. Apple bought back shares, mainly from Icahn, so that Icahn would go away. The buybacks weren't exclusively from Icahn, so it wasn't technically greenmail.