I've always considered the American name 'Chinese broccoli' to be ridiculous. Although both broccoli and what you call gailan (芥兰 - jiè lán in 95% of China) are both members of members of the Brassicaceae family, so are many other vegetables including turnips, kale, mustard, all the cabbages etc. I strongly advise disassociating the two in your mind.
I have no experience of "Americanized Chinese" cuisine. American-Chinese cuisine and Chinese-Chinese cuisine are two very different entities.
Broccoli is certainly used in regional Chinese cooking but not in the way it is used in America. I mentioned broccoli back in this post.
QuoteI’ve been known to judge a place’s ‘authenticity’ by the type of broccoli served. Am I wrong?
Yes.