I don’t think that a black powder Jones underlever was ever expected to shoot loose.
One thing that a Jones lockup provides is a positive block to the barrels moving forward. Thus, the resistance is shared by the hinge pin and the massive screw grip in the action bar.
Most later “bites” (think Purdey came up with this) in the barrel lump engage the rear of the lump offering nothing more than holding the action closed while the forward forces are borne entirely on the hinge and whatever additional bite was incorporated - doll’s head, Greener, Webley screw grip, etc.
Therefore, if the third bite wasn’t fit perfectly, the hinge did all of the work and over time could be worn out - battered.
I think the Bissell rising bite may have a sort of self adjusting aspect to take up any wear - would have to take a look.

My thought is that a Jones would loosen, not through the actual shooting, but through the thousands of openings and closings that could wear on the mechanism.
It is interesting to note that the Jones lockup is, in principle, very similar to the front lugs on a Mauser bolt action. A 90deg rotation drawing the action closed with what is really just an interrupted thread. The thread in each case being the lever lugs on the Jones and the front bolt lugs on the Mauser.