I used a 55 for a long time on a wooden stand, so I should have experience with a swaying tank, but I don't recall that as problem. Even when it was one-third full and I was leaning inside it doing maintenance, the stand wasn't swaying. At one third full, I would be able to push the stand slightly, but there was no sway. When full, I don't recall accidental movement. I'm sure if I had leaned into it like a linebacker, I could have gotten some movement, but anything less would have been ineffective.
IMO it's the stand. If the screws are not properly and firmly sunk, if they are the wrong type or size for the purpose (as a tank stand) or if a few critical ones are missing, that could be a problem.
What I mean is that it's one thing if the entire stand is moving as a fully integrated unit (bottom tilts simultaneously as the top tilts) and vastly different if the top moves while the bottom stays still (or if the left side moves while the right side is stable.) If the stand is moving that way, it's the joints, and then that would be an issue. Over time, the joints will weaken as it sways whenever it's moved inadvertently.
It's just not my experience that I could in any reasonable way move a 600 lb tank while it was sitting firmly on a solidly built wooden stand while on a flat surface. I agree that logically it would seem easy to do because it's narrow, but I don't recall any memories of it being an issue.