Exactly.
Under bruce they had the 15th largest wages in the league and when they stayed up under martinez they had the 15th, 15th and 17th biggest wages and then when went down they paid the 19th largest wages. The first time under the later two managers where they paid one of the lowest three wages they went down. That was something martinez couldn't cope with but Jewell who had the 18th lowest wages in both of his seasons, could.
The interesting thing about combining those two things from an outside point of view, is jewell spent 9 million net on transfers, bruce less than a million and Martinez made more than 11 million in the market. And the change seems to mean not less money being spent but rather a change of tactics. Jewell kept his team up (and indeed into the top half and to a cup final) while paying them basically championship wages (the third lowest wages in the league). By the time Bruce took over someone clearly decided that they weren't going to keep staying out of the bottom 3 without offering more money as wages than that as they wouldn't be able to either attract or keep players of the standard required.
Since then they've made an effort to be paying at least more money in wages than 3 to 5 other teams. (Though I suspect Whelan has a wage cap of 40 million and that's why Bruce left.) And they made up this money by not spending all their outgoing transfer fees.
Again I suspect Martinez had been told by Whelan that his wage bill has to be below 40 million and anything above 35 has to be funded by outgoing transfers. In short they were gambling that they're good enough at buying low and selling high to pay a wage good enough to attract players good enough for 17th. They're not gambling on a manager who uses tactics and motivation to get players on low wages to play better than the market dictates like they were under jewell (again they went down the season when their wage bill was one of the bottom 3 in the league for the first time since Jewell). The manager's main job, under that plan, is to raise money in the market, which Martinez and Bruce had done excellently in.
It was almost inevitable that when the other clubs around them started matching their wages without having to fund that by selling their best players that Wigan would go down, and so they did. Partly this can be put as a failing of the manager, Martinez simply wasn't capable of producing a team who over 38 games would perform better than their agents reckoned their players would, his team was basically the sum of it's parts. If he paid 50k a week to eleven players then his team played like a team worth 550k a week, managers like allardyce, moyes and jewell who favour organistaion and systems over individual brilliance tend to get their teams higher than the wage bill dictates, martinez didn't. But I think the financial situation was basically a strightjacket for him in that the need to sell to fund his own budget stopped him ever being able to advance his team as he had to tear it apart every year and it was almost inevitable he would fail eventually.
But the point was he was the only manager from wigan to not be given money for wages and also not be giving money for transfers so his job was harder than that of the previous managers and so you can't argue that he did a worse job than them, even if you ignore the FA Cup.