Great question. I can give ONE answer, not THE answer. Again, typical zen 
First of all, dharma questions are mostly handled by “transmitted” teachers, but it depends on the community, lineage and person. Someone might instantly defer to a teacher, while another will give a full blown dharma talk, you never know.
It took me years before I even stumbled upon the Canons, either Pali or Chinese. They were never a part of the discussion. In Soto Zen, especially, which is what I know, teachings are mostly based on either Dogen Zenji, the Chinese ancestors or modern teachers explaining the ones I just mentioned.
Most folks are familiar with Mahayana texts, such as the Lotus Sutra to one extent or another, the Platform Sutra, Diamond Sutra, Surangama Sutra, Lankavatara, Vimalakirti… I know a large number of folks who don’t even know where they could find the story of Shakyamuni’s awakening, what he taught about meditation, what the 8NP is, what the 5 hindrances are, what types of meditation can be found in the Suttas and Agama Sutras, etc..
There is also the aspect of not understanding the origins of different texts and stories, which is not hard to comprehend, given that if what one encounters first is a Mahayana school, then what they are presented with is introduced as THE actual word of the Buddha and things are defined from the get-go quite differently than what one may find in EBTs.
Because of how Zen developed and is approached, as “a special transmission outside the teachings, not dependent on words or letters”, there is not much emphasis on the sutras, as it is understood the Dharma holders, the lineage of ancestors from “the Buddha” to whichever one of us has received Dharma transmission, are equal voices of the Dharma to that of any sutra. It is a complicated dynamic, I would say, and difficult to explain in just a few lines. For a Zen fellow, the Dharma is not contained in the letters of a text, but in the lived experience, in direct awakening, in seeing into one’s mind and nature.
This answer is probably very poor and I apologize for that, but I hope it somewhat answers your question.