Swivel chair tilts

Thirty year old Staples wood veneer, black steel, grey cloth swivel office chair tilts about five degree forward left. Turned it upside down and tightened all the crews, nothing seems out of place. But when you look at the front it does seem to tilt five degrees forward right. There is a rivet perpedicular to the pedestal that attached the pedestal to the base, that does seem to move not even a centimeter inside its hole that might be responsible. This problem may be old but I seem to have noticed because a now gone knee injury caused me to pay better attention to posture. Is there any risk this thing could collapse? Instinctively, I think not.. but..