Viewing the car from the side, picture a large number of lines, each passing through the rear tire patch. Each line represents a particular value of percent anti-squat. The 100% anti-squat line also passes through a point directly above the FRONT tire patch and at a height equal to the center of gravity height. If the rear axle assembly is rotating about a point below this 100% anti-squat line, the car will squat; if above, it will rise. With a ladder bar, this "point" is the front pivot. So, yes, it's not at all uncommon for a ladder bar car to squat. With a 4link, the "point" is determined by the intersection of a line through the pivot points for the upper link and the intersection of another line through the pivot points for the lower link. With deflection of the suspension springs, this intersection moves, so it is referred to as the "instant" center.
Note that, with either a ladder bar or a 4link, the right side IC (instant center) does not have to be the same as the left side IC. This sort of adjustment is not at all "weird," but, in fact, can be used to counteract the unloading of the right rear by the driveshaft torque. If done properly, it is possible to have equal rear tire loading for any value of driveshaft torque. See my site for further information.