But you answered as a fact that a share buyback increases share price, and sorry but I don't agree with that point - as demonstrated, for an asset holding company it is not the case.
And for a company with cash generation capabilities there is still a subtle point about whether the company can create more value with the cash than the shareholders; if the company can create more value than shareholders, then removing cash from the company via a share buyback should reduce share price. If it cannot, then removing cash from the company should increase the share price.