I expect you to send the Eth back since it's never yours, before running away with others money always think about been in others shoe, what if you are the one that mistakenly sent out the Eth in the first place? Won't you wish for a refund?
This is true! There is a sentence that I always remember "treat people like the way you want to be treated". Therefore, try to be in other situations and think about what should they expect! Let think what if the one who mistakenly sent you 1 ETH has to borrow money from the bank or something to invest in this market? What if 1 ETH is all they have left? I would send it back!