It's somewhere in between those extremes. It's true that some things that go into a contract aren't actually valid because they infringe on rights or aren't within the authority of its parties. It's also true that some things are only valid if they're mentioned in the contract, because they might not be a typical part of doing business (e.g. things like fees or handling disagreements in arbitration hearings). It's also true that some things are implicitly in the agreement without being mentioned in the contract.

It's worthwhile to be aware of what's called the Reasonable Person standard. If you own a business it is worthwhile to be somewhat familiar with the corporation law in the jurisdiction the company is incorporated in. And it's always useful to have a lawyer you can ask some questions, if for no other reason than to have some chance of avoiding those expensive (in $$ and time) arguments before a judge. But I'm not a lawyer so don't ask me.