I don't think the restaurants are trying to "cheat" anyone of the miles; but I believe I read some Rewards Network material that indicated they keep 75 or 80 percent of the transaction as repayment of the money they have previously advanced to the restaurant (leaving just enough for tax and tip supposedly). So it's about their cash flow; your miles are no concern of theirs, that's between you and idine. However, I would be wary of any place making this kind of offer because it indicates they are barely hanging on and should make you wonder what corners they are cutting.

The original post was long ago, but I think the right thing to do would be take the discount and give everyone their fair share of it. The OPs situation seems similar to if a restaurant offered you your meal for free if you could convince your group to eat there. Chances are your friends are indirectly paying your subsidy, without being given the opportunity to choose to do that or not.

Edited to add:
The above description only applies to restaurants using the traditional idine financing offered by the company. The company has been trying to move away from that model to a "marketing" model in which the restaurant does not get financing up front, and pays a much smaller percentage of the bill to idine as a commission for idine steering the customer to the restaurant. I don't know what is the breakdown, what share of participating restaurants are in each category.