Not a good idea! They're right, propane is heavier than air, so if you have a leak, even though it is small, it will just flow out and fill the room from the floor up...big recipe for disaster. While NG isn't perfectly safe, either, it is lighter than air, has a special chemical mixed in with a distinctive smell, and goes up (and hopefully, out) where you're more likely to smell it should it have a leak. Either one can literally flatten a building, but it's more likely with propane. There's a reason you can't transport it through a tunnel, since they're usually a u-shape to get under whatever, it would just sit at the bottom waiting for a spark.
It's not only about interlocks, it's about an accidental leak somewhere. All burners contain something to detect if the burner did not come on, but with propane, each time it tried, a little more gas would accumulate in the area, eventually reaching a point where the next time, when it tries to light, it may just light up the room and blow the house up.
You could put it in an attached shed, but you'd have to fill the system with antifreeze (this decreases the ability of it to transfer heat, so you may need a slightly larger one), and it wouldn't be as efficient since the heat would be outside verses inside.