the need for those laws implies that our sense of fairness is not innate.
That is not true. The truth is that we have two competing impulses. We have the impulse to cooperate, and the impulse to cheat and get the best deal for ourselves.
Suppose we observe two strangers. They each do an equal amount of work, see them both get rewarded with food, shelter and other good things. We then see one of them got twice as much of these things (more food, a bigger, nicer shelter, etc.) for exactly the same effort. Studies are clear that even young children, across cultural lines, will see that as unfair and react negatively to the one who was getting the bigger benefit.
That is the innate fairness impulse at work.
Now imagine that *you* are the one getting the higher benefit. If the other guy cannot see what we're getting, we are likely to be happy with the arrangement and deny that it is unfair. That is the selfish impulse.
If the other guy does see and objects, we're very likely to acknowledge some imbalance, but compromise by only giving *some* of our excess gains back.
In a society though, there are a number of people around us, and yet only one of us. So when 'unfair" things happen they are more likely to happen to other people, which we find innately objectionable. Laws are only passed because we know we hate to see unfairness except when it benefits us personally. We have an innate aversion to that. Usually there are more situations where other people will benefit from unfairness than there are those in which we will benefit, so on balance we are happy to place a priori limits on them. If we had no innate sense of fairness, then unfairness would never upset us. We'd have no concept of "fairness" at all, let alone an emotional intuition about what was unfair. It's the innate sense of it that leads us to be mad when we see (other) people benefiting unfairly...and that is the impetus for passing laws against unfairness in the first place.
If you look online at the psychological an anthropological literature on fairness, it's evident that the sense in innate in most (if not all) primates, including humans.
As for what "innate" means, it does not always mean "always obviously on display". We have an innate instinct for self-preservation, but that does not mean that no one, ever, risks their lives. We have an innate capacity to love, but that doesn't mean that everyone behaves lovingly all the time, and competing emotions never conflict with love. We have innate affinity for pleasure, but that doesn't mean that no one denies themselves pleasure. "Innate" means you are born with the sense of fairness, without it needing to be taught to you, but that doesn't mean that competing impulses never override the sense of fairness.
