I think your concern about Levitt and Dubner is legitimate, though it would be more so if they published in Nature rather than blogging to Paul Krugman's audience.

The authors of the daycare study described the fine as "relatively small but not insignificant." Whatever the size of the fine, it still prompts the question of why customers consume more of a service when the price changes from zero to something positive. The answer seems to be that a monetary incentive drowns out non-monetary incentives, like guilt.

As Dan Ariely puts it in Chapter 5:

the theory of demand is a solid one—except when we're dealing with the price of zero. Whenever the price is not part of the exchange, social norms become entangled.

I give Freakonomics credit for tricking people like me into realizing that economics is pretty interesting. Sumo wrestlers cheat, prostitutes use pricing strategies, drug empires operate like corporate empires. The ideas that incentives matter and unintended consequences are ubiquitous are important and ought to be popularized.

Kidney sales are legal in Iran.

And Iran is, therefore, the case study. Apparently at one point there was a waiting list for kidneys in Iran: the donors had to wait for a ready recipient.