I used to shop at a grocery store near me that had a “kosher” deli. All of the food was premade outside of the kitchen. I obviously assumed that it was all kosher, it was all separate equipment. All the cold cuts were all under reliable heschers. I later found out the place has NO RABBINICAL SUPERVISION! The primary thing I bought was the rotisereie Chicken, which was under the Empire brand. I know for sure the meat is kosher because a special metal wrapping of the brand’s seal is always attached to the meat. I always made sure it had it on. The only thing placed on the meat was spices at a separate table. A few times I reheated the chicken in my oven. This place even sold the chicken in a special bag that said in clear letters “kosher.” All of my flatware and plates were boiled on Pesach, I have not bought a chicken there for about a year. But a friend just informed me that they were not supervised. They prepared the meat in a very transparent area that was open so you could see how they did it. Should I Kasher my oven?
If you know that the chicken that you bought were indeed kosher, there is no need for you to kasher your kitchen. Obviously you won’t buy there anymore, but it doesn’t mean that your kitchen needs kashering, as you don’t have any positive reason to assume that it was indeed non-kosher.