Thank you for a very lucid analogy. This seems like pretty basic stuff. Why would mngmnt do that?
When I was in graduate school (years ago at Northwestern)I had a finance professor that said that stock buy backs were the worst use of capital. He argued there was always a better application to increase shareholder value over the long term.
In this case, using borrowed money in effect, seems just slight of hand to increase or maintain some level of EPS, which would not occur otherwise through internal growth to artifically support the stock price.