Neil, you are right, Princesa has not deep red flesh. I have just realized of my mistake.
I have tasted my first true Princesa and it is not the fig I described in my initial post.
The fig which I described is the variety "Planera", also from Montserrat Pons.
The origin of my mistake are two labels I took from the soil beside Princesa and Planera pots. I put them misplaced, Planera had the "Princesa" label and viceversa.
I am very careful with identifications but sometimes black birds remove the labels from the pots when they are searching bugs in the pot soil. Usually, the label is only moved and remains in the pot, but in this case, the two labels were removed, and I was not right putting the labels again.
I keep my pots all year outdoor in my orchard, black birds "care" for them, removing labels and eating figs ;-)
Sorry for my mistake.