Legally, they can deny warranty coverage due to an aftermarket part or modification only if the aftermarket part or modification actually led to the breakdown. This is a provision of the Magnuson-Moss act. That doesn't mean that sometimes companies will try to use whatever they can as an excuse to avoid doing warranty work.
Something like a Banks chip could reasonably be construed as being a cause of many sorts of powertrain breakdowns, since it does inherently place parts under greater stress than the original factory settings. On the other hand, it should have no bearing on a breakdown in, say, the steering components.
