I am in a region where the winter daytime temp averages in the 30's and 40's, and the night time temp normally gets below freezing, sometimes down below 20 degrees.

Given that information, would you say it is necessary for an electric heat pump to have a working back up (i.e. electric elements, etc)?

I notice my heat pump uses it's backup heat quite a bit as it goes into it's defrost every so often.

The reason I ask, is because I got into somewhat of an argument with a guy who was leasing a house out to a family who's heat pump wasn't working. He ask me to to come by and investigate, being somewhat handy.

I'm not a heat pump expert, but upon looking at the air handler, I noticed that it has a gas backup, as opposed to electric. I also noticed it wasn't lighting. Knowing there was no nat gas service in the area, I suspected the propane tank may have been empty, so I traced the gas line and to my surprise, there was no tank, the line just runs outside and comes to a stop. It's not hooked up to anything.

I explained that someone is going to have to call a propane dealer to get a tank out here if they want the heat pump to work correclty. They didn't believe me.

So my question is, who is right here? Me or the landlord?

Usually a backup source of heat is needed with a heat pump system. Under the circumstances 20 degrees as a low tempersture the heat pump might keep up but if the heat pump breaks or fails then what are you going to do. So with that said a backup source would be a good idea.

Sounds like you stumbled upon one of those newfangled furnaces that just runs on outdoor air, no fuel needed. So cool, I want one of those... :D