We don't know if Wigan have offered more or less though do we?
We don't know if the Rovers offer was still on the table, Broughton may well have withdrawn it leaving Nyambe with only one option. He may feel that the offer to Nyambe was a good one and feels he can get better for the money.
There's a lot of assumption that Wigan have paid higher wages than Rovers without any evidence whatsoever.
Even if they have, it doesn't mean Rovers couldn't beat their offer, it could well be that they chose not to.