This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
I'm not a JavaDoc specialist, but if what you assert is true, then I'd say that you would want to declare the default constructor and based upon docCheck, you can have a simple one-liner to document it.
Another factor that comes into play is how much JavaDoc you are doing. I'm using the -public flag. If you are using JavaDoc at the package private level, then perhaps this is why you are getting JavaDoc non-comments for constructors to classes which are not public.
All in all, I attempt to not have anything show up in the JavaDoc which is not documented by me. And, using the -public flag may not be the norm, but it is what I decided to use.