You must have won the DeFrates Accounting Scholarship! The message said reduction in shareholders' equity not wealth. When you buy back shares you either reduce cash/increase debt and reduce shareholders' equity. DUH!
We have apples and oranges being mixed here. The journal entry for a stock buy-back does, in fact, reduces shareholder equity on the balance sheet, thereby worsening a company's leverage. The question is, what do you mean by "shareholder wealth"? As long as the company's borrowing rate is not too high, the buy-back does increase EPS, so a buy-back can be argued to increase shareholder wealth. However, as analyst Genco of Merrill Lynch noted, share buybacks so far seem to have done nothing for companies in this industry.