False, for corporations, share buybacks are not deductible as a cost and thus come from post tax profits. The main reason for share buybacks is it allows you to defer taxes until you want to sell [0].
We can't generalise to blanket statements like that, or the perfect company would never reinvest and would end up owning all it's shares. Not every company can reinvest and get the same benefits, or buy back it's shares and yield the same returns to investors. All taxes do is landscape the playing field a bit.
How is this at all the case? The second sentence is true in some circumstances, but you buyback for other reasons than interest rates, and corporate taxes don't affect how good or bad buybacks are.
[0]: https://en.wikipedia.org/wiki/Share_repurchase#Tax-efficient...