I noticed this too they definitely seem to have some withheld information and plan as to why they are making it public.
I suppose if the hunt/ publicity does spook the parents/ father it might mean they try and flee which in itself would make them more obvious as likely suspects as in the family at x address have done a midnight flit (is that the word) after the search details were on the news- big red flag.
Can DNA testing determine if both parents are related and to what extent ie cousins (legal) = less dna similarities but more than none cousins, brother and sister = maximum similarities , father and daughter = more than cousins less than siblings.
Lastly I think their ethic heritage has been mentioned before and can get quite specific so that would rule out lots of people immediately and make targeting the search easier surely so if for example they find the profile matches Uganda they can look into that community within the area etc.