No, it really is about right and wrong. If you allowed yourself to be dealt a bad hand, then you man up, hold yourself accountable, and learn from it. Too many people get suckered in to these bad contracts and insurance plans for XYZ system from the dealer because they do not ask probing questions about the terms of the contracts. Before I bought the road hazard warranty 6 years(100k) miles for $280, you can bet the finance guy got drilled with him showing me the various terms of the contract. If you allowed yourself to get taken advantage of, it does not give you the moral imperative to do something fraudulent to try to get even. You are simply being handed the terms of the contract that you signed on with.
What you can do is utilize proper channels to ethically get the problem resolved. If they wish to replace the tyre with a POS Chinese offbrand, then it is up to you to explain the liability that is involved with replacing just a single tire. Not replacing tires in pairs unless it is the same type can be extremely dangerous as it can result in your car pulling unexpectedly to a side, especially if you are driving in low friction conditions or you aquaplane across a puddle.