Interesting that you refer to an old press release, which dos not take away from the fact that whether you like it or not , and your opinion that it was different, primary responsibility for Control of the EU external border of a member nation rests with The member nation not FRONTEX, and where FRONTEX's role is defined in EU law. The opening of this office did not in fact change the role of FRONTEX as so defined in EC2007/2004 as at various times amended, including in 2013 after that office was opened, but to facilitate local performsnce if that role.
You have thrown around the phrase shared responsibility, but without regard to what the mechanism was and the legally defined role of Frontex in it.
Anyway now we have the verdict, reported here in a press release
http://europa.eu/rapid/press-release_IP-16-1627_en.htm
And with the decision itself.
http://ec.europa.eu/dgs/home-affairs/what-we-do/policies/european-agenda-migration/proposal-implementation-package/docs/20160504/schengen_proposal_en.pdf
You can argue till you are blue in the face about what you think the hypothetical position should have been, that is your opinion but you are certainly not the EU and all the documents reflect what those whose opinion counts, ie the EU Commission, and Council that GREECE Not FRONTEX Was resposible for border management and GREECE not FRONTEX was seriously deficient, and that not all the deficiencies have been corrected.
The French had reportedly taken their own measures, from 26th April, preempting the Official decision.
http://greece.greekreporter.com/2016/05/05/paris-airport-treats-greeks-as-non-schengen-zone-members/
Please argue with the French about that. They are no doubt sensitive to the fact that at least some of the Paris attackers came through Greece.