It is most definitely false to say that, in Arthur Miller's Death of a Salesman, Willy is a realist who tells Linda the exact truth about how his work is going as a traveling salesman.
We first see the falseness of this idea in the opening scene. When Willy comes home early from a trip, saying he had trouble staying awake on the road, Linda encourages him to ask for a desk job in New York, saying, "But you're sixty years old. They can't expect you to keep traveling every week." Willy's response is to be evasive about how badly things are going at work. He doesn't talk about the fact that he's only earning commissions and barely bringing in enough commissions to meet his household expenses. All he really says in reply is that he's their "New England man" and that if "old man Wagner" had still been alive, Wagner would have already promoted Willy to head of New York.
We see further evidence of the falseness of the idea of him being upfront about his struggles at work in Act II when he announces he'll go into his office to ask for a desk job, optimistically saying, "He'll just have to take me off the road." He even daydreams about someday buying a farm and building two guest houses. However, Linda brings him back to his senses when she lists the household expenses they still need to pay and says they are short. When he asks why they are short, she lists a few general excuses, but the reality is that he is short because he is not bringing in enough money with his commissions. In addition, rather than get the desk job he thinks he will get, his boss Howard fires him.