That debate you just had about legal positivism was fascinating, but it didn't really have much to do with the relationship between rules and reasons. Here are some simple truths about rules and reasons:
1. Rules divide into mandatory, permissive, and empowering types;
2. Permissive and empowering rules are not reasons to do what one is permitted or empowered by them to do;
3. But mandatory rules are reasons (or more exactly, the fact that there is a mandatory rule is a reason to do whatever the rule requires);
4. The reasons referred to in 3 are reasons of a special type, which give mandatory rules their special force.
5. Since not all reasons are of the special type referred to in 4, not all reasons are rules. (My original contention in the post referred to by Poohbear.)
Raz has done more than anyone else to explain the special type of reasons mentioned in 4. His Practical Reason and Norms (1975) introduces the category of exclusioary reasons. He argues that the type of reason mentioned in 4 is (a) a reason to perform the act required by the rule that is also (b) a reason not to act on some or all of the countervailing reasons. This combination is later dubbed by Raz a 'protected' reason.
Raz actually talks about 'norms' rather than rules but this shouldn't distract you. A rule is simply a norm capable of an indefinite number of applications to different cases. (Norms that are not rules could be called 'rulings'.)
There are mandatory norms (including mandatory rules) in every legal system. But not all mandatory norms (and not all mandatory rules) are legal. There are also moral mandatory rules, mandatory rules in games, etc. Raz differs from many other writers in providing a unified analysis of them all.
Hope this helps!
PS thanks for pointing out my broken link, Poohbear. I'll try to find a moment to fix it. Good luck with your phone interview.