And not only in this case. Spin has a connotative association of a sort of shady reinterpratation.
Like this-
"Even though we meant what we said when we said it, what you are supposed to understand is this is what we meant/mean now because what we said before is inconvenient/embarassing/illegal/etc."
That is the aspect of using the term "spin" that bothers me. There are other pejorative terms to use, this one is not accurate.