> So if Groupon stopped giving cash up front they shouldn't lose any customers they need, right?

That's not strong supporting evidence. Cash up front is one of the incentives that Groupon uses to acquire customers. Dropping it would certainly lose at least a few customers. They have a shit-ton of customers, doing many things would lose them customers. But it's not the core value proposition of Groupon.

Now if Groupon stopped advertising your business and discount to their enormous email list and only gave you cash advance in exchange for future revenue and they don't lose much business, then it starts looking more like what the OP claims.