Yes, good question. It can be more of a demand, even -- before you sign, ask "can you send me all of the documents I will be required to sign along with my contract?" and expect to be given the full run of corporate policy, non-disclosure agreements, etc etc etc. If they won't give them to you, they are hiding something and you shouldn't sign. Corporate policy should be incredibly boring and nobody has a good reason to prevent you from seeing that.

If you've signed a complete contract already, and there are new things to sign, they're asking you to agree to a new contract. Which you don't have to agree to, and if you don't, then anything you've already signed is still in effect. To get rid of you after that they have to resort to the termination provisions in the original contract. Of course "refusing to agree to corporate policy" is typically something that they can terminate you for. So a big part of the law dictating how much they can make you sign later is found in termination provisions. If your original contract's termination clauses are written so broadly that they could fire you easily for refusing to agree to a new contract that essentially rewrites the old one, then there are things you should see a lawyer about before touching it. (This is a much bigger deal than policy changes. I'm talking "no we actually have 10 more onerous pre-conditions to exercising stock options that we hid from you, such that you will find it almost impossible to do. sign here".) Large swaths of contract law are devoted to invalidating terms that say versions of "I can dictate the terms".

So my guess is that the horror stories were not supported by the original contract using likely-invalid language, but rather purely on the threat of messing up someone's new job. Especially if you're e.g. moving for a job, your goal is to sniff this out before you sign. So insist on full pre-signing transparency, get assurances that there are no other documents that are considered mandatory, and watch the responses carefully.

Indeed, you have very well summarized my thoughts on this. 100% that.

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.