If using tires as a container makes you jittery, use something else.
I don't have any old tires around here, but I grow most all my potatoes
the way she described, starting at the bottom with a few (3, usually)
chunks with eyes. Soon as they have a good start, I set a cardboard
box (with it's bottom flaps folded against the sides. and it's top flaps
folded down) over each group, and I've used tomato cages lined with
several layers of newspaper. All you need is something to contain
soil/hay/whatever as you go up. Doesn't seem to matter much if the
sides are high/solid (thought it might cut off too much light); the
plant is going up anyway.
If you don't mind hard plastic, you could set yourself up with the upper
portion of a trash can that's had it's holey, or cracked, bottom
removed. Really doesn't matter what it is. I guess concrete blocks or
something would do the job, but then you're getting back into the
lifting I was trying to avoid....
The tires do make neat looking 'cairns', though, and surely they would
absorb/hold heat if one needed that, but here we don't need extra heat,
so I just keep using boxes.....