But the Big Man (at least in other contexts) is conventionally generous. Lavishly so, but within conventions that impose, along with the generosity, certain obligations on the recipient.
Good point, I think the obligation side of that may be at play with the "punishing" example. It's possible that the sort of people that were recruited for the study were the kind that resented being obliged to give more than they were already.
Exactly this. The line from Lawrence of Arabia comes to mind: "I am a river to my people." The US equivalents are the mob boss (think of the opening of The Godfather, where Don Corleone hears requests from ordinary citizens) or the political boss dispensing patronage. In both cases, participation in the system of power binds the recipient into the system. Which generally increases the control of the Big Man over a resource stream.