This is the flip side of top athletes always trying to get top dollar, not because they need the money, but because the money (and how much they're making relative to their peers) counts as a measure of "Respect", how much they are esteemed in the baseball universe. It's the flip side because Dempster decided that he had all the respect he needed, and so the money itself - what use was that to him? After nearly $100MM in income over the years just from baseball alone, the dollars aren't driving him. If he were going to play, the money would be meaningful because it would represent "respect", but if he's not going to play, it's not meaningful to him.
That's my armchair-psychologist analysis of why he would willingly walk away from $13,250,000 rather than take the totally-legitimate avenues that were open to him to get that money without trying 100% to play his best baseball. He deserves a lot of credit for it, regardless, but I see it as a lot more understandable through that lens, rather than thinking of him (and Foulke / Gil Meche / etc) as a bunch of ascetics.