Kosher only filters for ingredients, not for processing equipment.

Late comment but this is incorrect. To be certified kosher, the plant is toured by a mashgichim for cleanliness and cross-contamination, all source inputs have to be identified and explained. Personally dealt with this for chicken and corn syrups. Coworker almost got us banned from Kosher chicken plant by bringing in McDonalds while we working on a project. We were give cafeteria cards and required to eat there after the incident.