Just ask yourself, "what are the odds a programmer and a recruiter would miss a contract I needed to sign?" Remember, there isn't a representative from the legal department in most interview processes. It's really easy for the people that are doing the interview to mess up stuff like this, because asking to see the contracts is an unusual request, and there's little consequence for them if they mess it up.
Sure, hence you ask to see all documents you have to sign before you sign everything. And make sure your contact states that with signature everything is signed.