Indeed, F1's official supplier and the Brackley based team were officially reprimanded for the Barcelona session.
But if the FIA's clarified guidelines are followed, Pirelli's contract with the sport actually permits tire tests with individual teams, and motor sport boss Hembery admitted he is keen to organize another.
Despite the controversy, and the fact Mercedes was penalized by having to sit out the recent Silverstone test, Hembery called that 1000km session "the best we've ever done".
"That's why we want more of it," he told Germany's Auto Bild.
"Maybe we'll do another 1000km test with a 2011 car," said Hembery. "At the end of the year we would also like to do one or two tests with a 2013 car — one in Brazil and a rain test at Le Castellet."
It is yet another clear indication that, although not entirely certain, Pirelli will be staying in F1 beyond the end of its rapidly-expiring 2013 contract.
But amid the delay in getting a new deal signed, the normal September 1 deadline for revealing the following year's full tire specification to the teams will blow out.
"We will inform the teams on October 1," said Hembery, revealing that the deadline has been extended.
Pirelli is tipped to produce wider rears for the high-torque V6 engines next year, but otherwise Hembery has hinted that the construction and compounds will be much more conservative than the controversial 2013 tires.
He said the scandals and criticism were "too much" this year.