I wasn't really suggesting "rules" as in "rigid laws we must follow" but rather like a set of rules to a game. Think about it for a moment. What differentiates one game from another are the rules to that game. That's what I'm saying when I ask "what rules define your relationship?" There are certainly "rules" that define a loving relationship, for example. "Be honest" is just one rule that helps define a loving relationship.
Every fun game has rules that define how the game is played. Without setting up "guidelines / rules", it's hard to keep things open and honest because you don't know how the other person will react necessarily. That's especially the case when one (or both) partner has a history of betrayal or trust issues. Rules may be for the distrustful, but there's also another side to it. Rules also help foster trust because it helps put people on the same page. Rules define expectations for both sides and foster good communication.
Rules, in my view, are a means to create a "construct" within the relationship that can foster a loving environment that minimizes jealousy, confusion, secrecy, etc. River talks about "agreements", but agreements can only be made when both sides can openly communicate about anything and everything. The "rules" in her case, are implicit. Although I totally agree with everything River has said, she (I think River's a she?) seems to be offering that advice under ideal conditions where the rules have already been established through a history of openly communicating. Few relationships, in my experience, are in ideal conditions.
Communication and trust issues arise in almost every relationship, and to find a relationship where you can communicate openly and honestly is not an easy thing to do.
Rules can be as simple as saying, "If you do X it will make me uncomfortable, so please don't do it. Instead, if you do Y, I'll feel much more comfortable." It may be an agreement, but it is also a rule that if broken will ultimately hurt the person who defined it. The rules require a dialogue and a degree of open communication. Agreements are made in response to the rules. For example:
Rule 1: Be Honest with one another
Rule 2: Don't keep secondary relationships a secret
Rule 3: Talk about your feelings, especially any jealousy
Rule 4: Maintain an open dialogue and strong communication
Rule 5: Respect each other's feelings and work together towards resolving issues
From those rules you can then make the agreements, which then fosters trust. You see, rules don't merely come from a place of mistrust. They help define the relationship and can actually foster a deeper level of trust between partners. They can also come from a place of love (which is what I think River was talking about).