Correct. Calcite, though not attractive in the same way aragonitic nacre may be, is very important in the early development of molluscs. While calcite is the bane of cultured pearl production, in nature it's important in juvenile and mature to over-mature individuals to maintain shell thickness and strength.
Fireball pearls are generally mature pearls, hence it's not unreasonable to occasionally find calcitic patches.
Sometimes these layers can be peeled away, but it's not with out risk of damaging the underlying surface.