Many many parents with a child with SEN or ASD do not get a diagnosis easily and spend a great deal of time (usually years) trying to get a diagnosis. What drives them to get help or a diagnosis is an understanding that their child is not developing in the way an average child might.
So while they are in that awful limbo of having a child who may not have the immediate appearance of having any SN or any actual diagnosed condition, they spend years listening to other parents with NT children tell them that they are neurotic (or worse bad parents if the SEN involves behaviour problems) and that their children will be fine with time and better parenting.
Of course some parents spend too much time worrying about something that will probably be fine in the long run but sometimes that worry has a basis and should be listened to.
As with most things in parenting, a general statement like the OPs is worse than useless. It does nothing to help individual parents with worries about their children whether they have special needs or not.
Some parents do overworry but some (and I include myself in this) spend too much time in the early years saying this sort of thing so as to appear non neurotic.
I would say in many ways I am quite a laid back parent but I also think that in my circumstances this made me a worse parent than I could have been by being a bit more "neurotic" For other parents being more "laid back" would make them a better parent.
However the results of a parent tending towards "neurotic" or "laid-back" in any particular instance is almost never apparent immediately but becomes more so in retrospect. Because of this I am completely unable to say for sure whether a parent is being too neurotic or too laid back in any particular situation.
I can only listen to their concerns and try and help with the problem they have in front of them and possibly share what I would do (if asked) but also understand that I have no better idea than the person asking what the best thing to do is.