Clinton shift might be correlated with paper vs. electronic ballot but it looks like districts that opted for electronic ballot have different population groups compared to the ones with paper ballot. Once you control for that, e.g. race and college degree, paper/electronic ballot correlation disappears.
To be fair, data sample is rather small so small effects might be difficult to pick up.
But controlling for everything is almost impossible to be perfect: designated location vs county wide, income, race, education, Trump/Clinton modeled support.
You'd have to pull actual voting returns by individual for those voting locations and states, and then have a good vote file. Then you can start to control for those variables and I would bet almost everything I have that doing so would reduce any irregularity these scholars are using as an argument that the election was somehow hacked.
In the past he mentioned using excel with various addons, and these printouts look very, grid like.
That's actually NOT for you to say. Rationalizing why it's not without doing the analysis yourself doesn't buy you that right, even if you read it somewhere and it sounds good.
It's easy to say you have to go a level deeper to get the truth, but at some level you have to accept the legitimacy of a source. If you don't trust Nate Silver, you can run the analysis yourself. You then have to choose whether to trust the source of the data. If you don't trust that, and you have the ability to to go the pre-aggregated data, you can go to that. Do you trust the people reporting that? At some point,it's not feasible to follow the chain of custody all the way back, so you have to make a call as to what level you are willing to go back before trusting the source.
If someone trusts the integrity and competency of Nate Silver, then they should be able to apply some level of assurance to his results based on that. If you don't trust Nate Silver's results because you doubt his integrity or competency, or even if you think it's just too important to trust to a single person, then speak to that, not to some simplistic and often impossible to satisfy ideal of determining everything yourself from pure sources.