I agree with your analysis to a certain extent. If you put the DI on the blade close to where it is contacting the work I would think that there would be nil downward movement on the front side and measurable upward movement on the backside.
Actually, just the opposite occurs. On the front side, the blade moves down, then up, then down and so on. In the rear, it doesn't rise up as far as I can tell. I suspect most folks who believe the tool moves in the rear have not used such a tool.
It isn't that the backlash is the culprit; it is the structure of the lathe itself - the cross slide, the compound and the slack in the slides and gibs that causes movement. As Savarin pointed out, replacing these structures with a solid plinth all but eliminates the issue on his lathe and I can guarantee you his lathe has backlash. If you dial into the cut, that essentially eliminates backlash anyway.
The difference between the front side and backside is that on the front side the blade can't move down. The blade can only move into the work as the backlash is taken up. The slight upward angle of my parting tool holder aggravates the problem. On the backside the blade is free to move up as the backlash is taken up. Instead of getting jammed into the work it rides up over the work.
On the front side, the blade definitely moves down, and it moves down in spite of any backlash you might have. It is the gaps and slack in the compound/cross slide system that allows the blade to move. To clarify, backlash enters the picture when the tool moves into the work due to slack in the threads in the nut and screw but when parting, you are feeding in and there is no slack in that assembly so backlash is not the issue; movement in the structure is the issue.
The upward angle of your tool has nothing to do with the issue provided the tip is on center. Many of us have those crappy holders that angle the tool up at an angle and have no problems parting with it. In a rear mounted tool, the tool does not move up as many think; it just cuts.
Why I am going through this mental exercise is because I don't think that I have the skill level to make a backside parting blade holder for my lathe. It would require machining precise parallel dovetails, fitting gibs and somehow attaching it to the cross slide or the cross slide lead screw. I think that I would be worse off rigidity wise than what I have now parting from the front side.
Chuck, I have no idea what kind of lathe you have or what it looks like. I can tell you that if I could not fabricate a rear mounted parting tool holder then I would consider a solid plinth to replace the compound and I would make a parting tool holder that holds the blade horizontally instead of at an angle. I would also spend some time adjusting the gibs between the saddle and cross slide to eliminate as much play as possible while maintaining freedom of movement.
For me, a parting tool is an important tool to have. I use it to cut grooves, demarcate and denote the depths of cuts and I also part with it. This is one tool that must work and I would do all I can to make it so.