It think its hard to determine from looking at a picture unless you can't see the top of the wheel. I think that's what Andy is looking at. In your case it your wheels look a little on the low side which would indicate a worn axle.
Look at www.inlandrv.com
which is Andy's site and it will explain what to look for - basically there is a swing arm that is attached to the frame and also to the wheel - looks kinda like a bone - if the arm is pointing up from the frame, good chance its worn. Another test I like, is if there is anyway you can find a new Airstream dealer near you is go inside a new unit - get the feel of what it should feel like and see what the unit you are looking at feels like. If you can't go into a new trailer I would still bounce around it - should not be stiff. Another question I would ask the owner is how much the unit gets used - a sitting trailer (like most of us) will get stiff if its not used.
If you can get the owner to e-mail you a picture of the swing arm that might save you a 700 mile trip.
Having said all that, I would just figure the unit needs a new axle and figure that into the cost of the unit - I think new axles brings up the trailer to basically a brand new unit - especially if you buy all new brakes/bearings etc.
Keep in mind a worn axle will not prevent it from being towed nor will if fall apart on the highway - just make for a rough ride on the trailer.