Consider:
It is really miscounted.
I think it depends on the particular context, but should it be the following?
It really is miscounted.
robertd
[ Editor ]
It depends on context, as you say. "Really" falls somewhere between being used as an intensifier (like "very": It's really hot in here!) and being used to mean "truly" or "in actuality".
My instinct is that there aren't varying degrees of "miscounted"---This is more miscounted than that sounds crazy---and for that reason I agree with your rephrasing, since it moves the intensifier away from "miscounted".