I think it's much more subtle point than buy-backs increase share price, otherwise it opens up some basic arbitrages. The point is, the share price already incorporates the value of the assets used for the buy-back, so buying back shares increases earnings per share but reduces asset values (and future earnings from leveraging those assets) and the two effects offset.
Simple example:
company A has 100 shares outstanding and only 1 asset: $100
The value of each share is $1.
It then decides a share buy-back is a good strategy, and buys back 50 shares for $50.
It now has 50 shares outstanding and $50 of assets.
Simple example:
company A has 100 shares outstanding and only 1 asset: $100
The value of each share is $1.
It then decides a share buy-back is a good strategy, and buys back 50 shares for $50.
It now has 50 shares outstanding and $50 of assets.
The value of each share is still $1.
The buy-back has no effect on share price.