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Can a model with Slow and Purposeful fire at full BS if it's in a Raider that moved 12"?

Look at the Passenger rules in the BRB. Quote the exact rules you're having trouble with.

The rules for passengers treat Combat and Cruising Speed differently. For the first, they would not be affected. The second they would. See, they didn't move or count as moving, like in Combat Speed, but are affected by their Transport going Cruising Speed. Slow and Purposeful does not override this.