based on my limited understanding. there is no clear dinal to certain sutras in Zen, that is just personal view, and what is more important is Zen is practice pattern of East Asian mahayana buddhism, just like tantric practice for Tibetan buddhism. all zen orders are sharing basic mahayana scholarly tradition and ritual tradition as well. in fact, westernized zen, which practiced in "centers" may be only emphasizing "the pure zen practice and meditation", but, Asian zen sects are enomoursly hybrid in actual ceremonies, a Zen monk would meditate 14hours during retreat, but in daily life he/she would read Amitabha sutra for ceremonies. and Asians would take it for granted. nothing strage here..
but generally, zen sects put empasis on Diamond Sutra, but except japanese zen sects, all of East Asian zen monks in China, Korea, Vietnam must study various sutras for many years , that means in Asian countries, scholarly cultivation and practice are interconnected very closly. there is no independent ZEN(Zen of the zen, zen by the zen, zen for the zen) in Asia.
and pure land tradition and zen tradition are merged each other very well, especially in Chinese, Vietnamese, Japanese Obaku-zen order. there is not dissonance at all. but if someone would practice pure-land zen(meditating while calling buddha's name in mind or with mouth) he/she mostly consider the pure land as the status of dhnaya. but if the same monk read Sutras in funerals, he could take the pure-land" as real. so Asian way of thinking is very flexible compared to western one