It's possible, too, that there are elements of the ship that use non-baryonic matter. Perhaps some components like warp coils use a form of exotic non-baryonic matter in their construction. Verterium or cortenum might be non-baryonic matter that helps drive the ship's subspace field stuff. In which case stray neutrinos and what not getting caught in it might cause problems.
This doesn't quite explain why they need to dose down the entire ship with something that kills all living things, but given how important subspace field manipulation is to Federation technology, perhaps there's elements within the ship's systems that like isolinear chips or something that also use exotic matter.