At age three this is totally, utterly typical. He is told about rules and "you can do this, don't do that" all the time, so his behavior in policing other kids shows that he is internalizing those lessons. I have seen every three-year-old I know do this! He will indeed get past this stage; other kids will (as another poster rightly put it) tell him "You're not the boss of me" and so on.
Is he in preschool at all? That's a great place to learn that getting along with other kids doesn't mean being the rules cop -- but it does mean knowing that vital difference between "tattling and telling" that others have mentioned.
You do not want to make him feel that he needs to clam up to the point that if an adult needs "telling" he should not tell. It's time to work with him on the difference between when he's tattling and when he needs to get involved and tell an adult. This distinction is very important; it helps protect kids when someone (another kid or an adult too) instructs them "Dont' tell on me" but the kid knows, in his gut, that someone should be told.
If your concern is that he's telling other kids directly what to do -- that's typical, and again, the other kids will sort it. He will figure it out. Just reiterate that parents and teachers are there to watch the other kids' behavior and if he sees something really dangerous (and you will need to work with him on what "really dangerous" means) then he should say something but otherwise he can trust that teachers and parents are doing their jobs. (If he is being hit or teased etc. of course he does not have to wait for an adult to notice it before he tells another kid to stop --make sure he realizes that.)
I would not ever use "Nobody likes a rat." He's going to see himself negatively if he follows the rules, and the statement does absolutely nothing to teach him that there are gray areas where he does, absolutely, need to tell an adult about what he sees, and there are times when he needs to tell another kid to stop doing something that is imminently dangerous. Your friends are essentially training their child to say nothing, when what prevents bullying is -- saying something!
Get some books that feature discussions of "tattling versus telling" and find ways to talk about that, but don't over-criticize him for being a "rat" or internalizing the rules. It is far preferable to the kid who never realizes that rules are for him! And if he's not in preschool, consider doing it next year so he has a year of a good (part-time) preschool before he enters kindergarten. Preschool is for working out these kinds of dealing-with-others issues that kids this age have, before they are in K, where the academic pressure today means that teachers do not have time to spend on things like this.
One last thing -- What's behind the concern that he will be seen as some kind of bully if he tells other kids to follow the rules? The term bullying gets tossed around a bit too freely these days. I grew up in the 70s too and in those days he would have been called the teacher's pet, not the bully! The bullies are the ones who never manage to internalize any rules--not kids like yours who are learning them and just applying them the way a three-year-old would.