Perhaps he buys a regular fare ticket at a deep discount, on a miles-rewarding credit card, upgrades it to first class using miles, then pays the cost of the original fare using some other mechanism that requires use of the miles to be remunerative. As the article mentions, finding anything wrong with the aircraft could be converted into a $200 or $400 credit.

By invoking certain rules or offers, you can actually get many more reward miles than the actual distance of the flight. That's why a large part of the practice is spending as much time in the air as possible.

Using those near-currency credits to bribe the airline employees with the airline's own stuff is likely another key part of the "fly free" strategy. The employees have some discretion in how strictly they enforce their employers' rules. Make friends there, and you have an easy flight. Make enemies, and you will have trouble.

There has to be some mechanism that makes this works for them, otherwise they wouldn't be doing it.

This article reminds me of one I read wherein a Chinese man bought a first class ticket for gratis access to the airport lounge, ate there for free, and re-booked his ticket for another day. Months worth of meals for the cost of one fully refundable first class fare, and he never explicitly broke a single airline rule.

This is just extreme couponing. This is the airline equivalent of walking into the checkout at your local grocery store with 3 carts full of stuff, and walking out after getting change back from your nickel.