2000 Toyota Corolla Exhaust Manifold

I had a catalytic convertor replaced two years ago and since my engine light came back on. I got a code 171 and secondary 420. They replaced both front and back oxigen sensor and another oxigen meter by the engine and the light is still one with the same two codes coming up. The dealear said that I need an exhaust manifold and a new convertor while the place that warrantied the converter said that can only be a leak at the manifold that can give a 420 code. Whom I should believe and how can I make the difference between having a leak at the manifold or a manifold broken? Would you please let me know if the manifold can signal a false 420 code?

Thank you