Since usage precedes correctness, I don't think it is really possible to know which is right. I agree with you however; it seems that "safe deposit box" is the more grammatical form. Safe in this sense would be an adjective, as in safe driving, or safe sex. Do you hear talk about safety sex?
In contrast, safety is ordinarily a noun. A rather abstract one which denotes a state wherein safe practice is being followed.
But I am afraid that in America, few people give a damn about what is right grammatically speaking, and even fewer would know how to approach the question. (T-Al is a prominant exception, and I hope he will weigh in on this thread.)
When I get billed for my box, the bank calls it a "safe deposit box". I think that means a place where you can deposit items in the expectation that they will be safe from theft. I would think that "safety deposit box" would suggest a place where gunsmiths might place safeties that they were holding for their gun repairs.
Ha
