Calabria tried to get a local Hechsher. That was their singular preference. It was the local establishment (and Basil's lawsuit) that did not permit them to do so.
They had no other choice but to find one that would allow them to make Kosher pizza, even though it was across from Basil. Clearly was not a "kosher-ingredient/supervision" issue...
Do you have intimate knowledge of the FACTS.
I don't go to either of those places, but I recall seeing some psak from a beis din regarding Calabria (shape of Pizza, etc.) I don't know if they comply with that psak or not, but I can fully understand no reputable Kashrus organization wanting to certify them while in legal dispute.
This gets even more political when considering some of the people involved here, but let's not even go there.
I have stated more than once above, that this is not a question of whether the food is Kosher, it's a question of whether it is certified so and if yes, by whom.