What birth stool were they using?
I use a stool a lot. Almost every birth, if not for the babe then for the placenta. Mine is a homemade wooden one. I do not seem to notice extra swelling or tearing on a stool. The yoni is more isolated and visible, of course, on a stool and gravity/pressure can make the yoni seem pretty full.
I don't think it causes swelling but it may increase a tendency to swell. Does that make sense?
Frequent, stand up and stretch it out, breaks should be encouraged to avoid any undue swelling,just as you would encourage change of position otherwise.
I like the stool for a break in mama having to hold her own self up in the pushing phase or for a change of position and it is a wonderful way to get baby around that pubic bone. Maybe not getting on it too early is the key..
Was mama directed to push or was it spontaneous?