Interesting you should think that, Alice. Do you think they will be refused leave to appeal?
I think an application will be made because the Drs McCann have no choice.
Quite how the Supreme Court will deal with it is another matter. Courts at that level, in whatever country, are usually only concerned with major points of law, which may be confused in the broader sense, which require clarification, judgment and ruling by senior advocates.
The only confusion on here is that we don't understand Portuguese law so we are really in no position to make a valid judgment on the ins and outs. Googling doesn't count !
For example the judicial secrecy bit. My understanding is that it is not a brick wall and to an extent at the discretion of the examining magistrate ie if he wants something "leaked" he has the authority to do it. Which imo puts it, as a crime, in the same bracket as in days gone by of not signing your driving licence. No one takes any notice unless you get lippy with the law then they do take notice.