I have a rigid fork, I have rims with I think about 25mm ID. I use Schwalbe Racing Ralphs at down to 20psi and I don’t get any roll in corners. I usually run a bit higher if I have lots of road to do (23psi) because I get bouncing on pedalling. 20psi is the best pressure to deal with rocky Welsh trails.
I used to use the Specialized Slaughter/Butcher combo (non-Grid) and these were terrible for bouncing and rolling, I had to run 30psi. So I think that Schwalble tyres have much more supportive sidewalls than the Spesh ones did. I use 2.2 Rocket Rons on my FS XC bike on narrow XC rims and they only need 25psi to behave well.
I’m no whippet either at 90kg and I don’t mince the descents.