I really hope Chang's story won't bite them in the ass later on. Like after Cash-Granny defeated Hyodo in a game of Sudden Death Bingo and she insists that all the money gets divided up to the non-existant coworkers of Chang and Mario
Well to be fair going to an underground casino is not exactly the same as the life or death gamble that they actually did together. Technically only Kaiji went to a casino that night.
I think they're also really downplaying the scale of money they won - she's probably picturing something manageable enough to just get deposited entirely into their accounts, not something they needed to transport on a truck. Since they don't want her to know how much it is, they needed some other cover story for the deliveries.
I think the idea here is that they needed a reason for the amount of bank cards. I guess the trio thought that the story about the coworkers would suffice, and the casino story is just a spur-of-the-moment thing Kaiji told her because she still wasn't satisfied. It also makes them sound better if they say "we did this for our bros" rather than "it's all ours!"