I think the issue is that you are taking too much on faith the description of the details of the experiment described in that link you initially posted. Notice that the website author does not post citations directly referring to the results described there .. all of the citations are to "related" experiments, like the one analyzed in the link I posted.
To my eye there is a lot of fuzzy thinking/analysis going on in the link you posted. For example, there has to my knowledge never been an experiment that worked precisely as he suggests with the cartoons he posted. Specifically, I do not believe anyone has ever measured the same particle both as it traversed the slit, and later at some projection screen. More generally, I do not believe that such an experiment *could* ever be done with QM particles in a meaningful way, due to the complications of carrying out multiple measurements on the same particles.
All of the experiments that address the issue of delayed choice and quantum erasers involve clever tricks with how the particle is measured *after* it has gone through the slits.
At any rate, I don't believe any of the allegorical accounts involving erasing data from hard-drives or the choices of visiting politicians, etc., without solid documentation in peer-reviewed literature, which I guess doesn't exist for those accounts. At least it is not given on the website you linked.