I've had absolutely no problems with stability in any way. I expected more "give" because it's on padded rails, but the weight is spread and you can't notice a thing.
I store my top on-end, vertically, behind a tall bookcase which has been strategically placed about 6" away from the wall. Although it was next to a couch, nobody noticed the gap, or the black tabletop. This was a 1-bedroom apartment in midtown Manhattan, and nobody could figure out where it went.
It stands behind the bookcase on the strong edge and leans on the wall or the bookcase just fine - I only had to be careful when getting it out or taking it on/off the table. Because of the length combined with the weight, I can't do it alone - I'm 6'5" tall, weighed about 230 pounds, would deadlift over 300 pounds, but couldn't handle it alone without risking damage. Very unwieldy. My 110 lb ex-wife and a similar friend could get it on or off the table just fine, but it was too long and unwieldy for me to handle alone.
But once it's on, absolutely no worries.