IMO, yes the stock must be held by friction with the wall. The inside of a meat grinder chamber has a certain amount of ribbing that assists in increasing the friction. The only reason that pressure increases is because the incoming stock is being 'overfed' at a higher rate than the screw is outputting at the plate.
I once worked on a grape press that was just like a giant version of a meat grinder. This press had been adapted for use in seperating honey and wax in a honey operation. The designers of this press had added a lobed gear, which engaged the main screw, something like a worm and gear assembly. This lobed wheel was near the input end of the screw and its axis was crosswise to the screw axis. The purpose of the lobed wheel was to 'shut off' the flow of material that wanted to bypass over the top of the screw. This also caused a positive flow of material to build up in front of the lobed wheel, and the effect carried all the way forward to the front of the main screw extruder plates. The pressure buildup caused honey to flow out through holes along the main cylinder of the press. The wax went through the extruder plates at the output end of the screw. In this application, I guess there was no way to get enough friction from the stock to keep it flowing through the screw, so I guess this was their solution.