This doesn't account for low information investors, though.

To buyback stock the company has to make an offer that enough investors are willing to sell. Once investors start to do so at these higher prices, the stock price goes up.

To the low information investor, this looks to them like the stock is worth even more than it was before, because it made money for them (on paper, at least).

And what about index funds? Regardless of the number of buybacks, the index fund isn't going to sell. This would also cause the stock price to rise.

This idea that a stock buyback doesn't affect price only works in a market where everyone has perfect information. In real life this isn't the case.