I do some handbuilding, ( I get odd ideas from time to time which have to be appeased and I have a couple of things in the pipeline now as it happens) but I really prefer the symmetry and balance of a thrown item.
Just to add: I have no trouble with joins coming apart in firing but I've seen it happen several times to others in my class - before you actually make the join the slip must still have a wet shine - it's no use making a long join and taking so long to apply the slip that it's dried before joining - if it has, apply more slip, (subsequent coats will take longer to dry, giving you a little more time) it must look wet before you join.
I watched the video too: in that footage the thrower knows that the wheel is not level and therefore ensures that he's working perpendicular to the wheel.
If he wasn't aware that the wheel was out of level and just worked perpendicular to where a level wheel should be, then one side of the pot will be longer than the opposite side, and the base won't be parallel to the top.
If the wheel was out of level but you were pulling straight up, the effect would be that the pot would get wider, not that you would get one side taller than the other. It's no different than if the wheel was level and you were pulling outward. Unevenness at the top is a result of poor centering or uneven pressure during pulling.
I was thinking that the extra length would be at the bottom.