How is Open Reading Frame (ORF) chosen?
Tl Dr: In the rosalind example they are showing the 3 reading frames that stem from the definition of a reading frame(non-overlapping triplets), not an example of open reading frames. Open reading frames are non-overlapping triplets between a start codon and a stop codon.
Its important to step back and understand what is meant by reading frame first.  It has been determined experimentally that translation occurs in non-overlapping triplets.  That is to say that if the ribosome starts reading at position n it will translate n, n+1, and n+2 into an amino acid, then it will start at the next non-overlapping position which is n+3.  For example, in the sequence: ABCABCABCABC if you start at A it will read ABC ABC ABC.... But if you start at B you will have an equally valid reading frame by the definition of a non-overlapping triplet and it will read BCA BCA BCA.  If you start at C it will read CAB CAB CAB.  What would happen if I start at the next A? ABC ABC ABC... See how you are back in the first reading frame?  No matter how long a given sequence it will only have 3 reading frames.
Why does that matter if they all start at an AUG?  You don't know which AUG translation starts at.  Not all AUGs are actually used as the first codon in translation, in fact, most are either internal to a translated protein or not translated at all.  An open reading frame is any sequence starting from an AUG to a stop codon.  An open reading frame can be within another open reading frame. E.g: AUGCTAUGGCGAUGUUAGAUGA. All of the valid open reading frames are:
    AUGCTAUGGCGAUGUUAGAUGACUAACUAA 

    AUG CTA UGG CGA UGU UAG
         AUG GCG AUG GUU AGA UGA 
               AUG UUA GAU GAC UAA
                      AUG ACU AAC UAA