It certainly happens. I don't know how commonly and suspect I may know an unrepresentative number of cases due to my work but I definitely know a number of examples.
More extreme cases include:
a child who had been to many different schools by the time they were in their early teens - every time the school raised concerns the parents moved them elsewhere. The child was very clearly significantly autistic.
a child who, at many years older, presented as an NT 4-5 year old socially, academically, emotionally and in some physical aspects. Parent in such strong denial that, when it was suggested that a specialist school would be appropriate, they said 'but if they go to a special school it's going to look terrible on their university application.'
a child who presents with completely stereotypical, classic aspergers - every single pointer that so many people assume are always present in ASD but actually don't have to be at all is there. Although very academic, child struggles massively socially and is bright enough to know and feel that nobody accepts or likes them. I'm sure the support that might come with diagnosis would help. But it is impossible to even hint at a problem with either parent. Their child is their child and is their perfectly individual NT child. A suggestion of anything else equals brick wall.
Obviously, in cases like that, the parents, though I understand their anguish, are almost certainly harming their child by not acting.
But, in more blurred/minor cases, I don't think it's always so. Eg:
A family of a fair number of children. All have things about them that scream aspergers. But all seem to improve (or learn to deal with it, who knows) as they get older and one parent says they are exactly like them and therefore they will be fine. All the children are coping well academically and socially so, really, who's to say those parents are wrong?
A SENCO has recently suggested that my 13 year old DD has ASD. Personally, I think she's wrong Certainly, my DD has an eating disorder and is a very anxious child but, although I cannot and would never try to deny that she has mental health problems, to my, not inexperienced, eye, she is totally NT. I don't see the signs for ASD at all. Does not agreeing make me irresponsible? I don't know.
This recent experience has led me to wonder if the diagnosis of ASD can actually be objective? I suspect it's so difficult to get diagnosed at times purely because it is subjective and some people see what others don't, see things differently etc.
I've also come across children with a diagnosis that has left everybody around them scratching their heads because we just can't see any evidence of it. Whether or not they're misdiagnosed or we just can't see the problem that is there I don't know.