Perhaps 'slamming into' is a bit dramatic, so maybe 'riding up' on the groove walls is more palatable. Of course this is just centrifugal force, similar to riding in a car down a FLAT (no embankment) curvy road, where you slide in the seat back-and-forth around every curve - pressing against either the car door or the center console. The stylus will alternate riding up on the groove walls as it moves back-and-forth with an off-center record.
The February 1959 issue of Popular Mechanics has an article titled, "Hi-Fi Buyer's Guide: Tone Arms", which mentions this concept, and warps as well.
"Vertical motion of the record surface, due to warp, works against the arm's inertia to send tracking forces skyrocketing. Back and forth lateral motions of the arm due to record eccentricity produce destructive side forces with a high-inertia arm."p.215
Regarding viscous damping of tone arms, "On warped or off-center records, it offers the same drawbacks as high-intertia arms."p.216
Clearly, heavier tonearms create more of an issue with warped or off-center records.