Just because some area (or one company) ignored the code for decades does not make it legal, I see HVAC NEC violations all the time.
Its a 'emergency switch' with a required red cover stating that its an emergency switch, how could that not be part of the safety system required by the NFPA oil burner code?
Looked it up in my code book (2017) and it could be that some AHJ may accept romex it says "or otherwise suitably protected" after the wiring methods.
Regardless of the wiring method the class 1 safety circuit begins at the 'emergency' switch any oil burner tech should know that.