State Certification (of the vote "integrity" and tally) is an entirely different thing than Constitutional eligibility requirements.
I read it the same as you.
But what struck me is that the attorneys have determined (on their own I am assuming) that Brown meets the Constitutional qualifications to hold elected office without Brown having submitted any evidentiary proof, since there are no laws requiring him to submit qualifying documents.
If my assumption is correct, then the attorneys arrived at that decision based on their own assumptions rather than evidence. What convinced them that he is Constitutionally qualified? His current position as a State Senator? The MA SOS certification of his name on the special-election ballot? Public domain information documenting his residency in MA and his apparent age?
It sounds to me like Obama was “qualified” using the same assumptions and lack of evidentiary proof. They apparently deem those assumptions to be sufficient and legal.