FWIW I'm not totally convinced that the paper isn't also anecdotal. They selected for people who would agree to have their internet activity spied on in exchange for extra credit, and then from that group selected only for people using the internet -- not their computers, but the internet! -- in more than half the lectures. And did all of this in a large enrollment undergraduate gen ed intro course with lectures that lasted two hours.
Sure, the results pertain more to excluding the internet from the classroom, but really that's just splitting hairs imo
1) people who are more informed care more about privacy
2) you become more informed by being the type of person who seeks out and successfully obtains information and not being distracted
If 2) and 1) hold, your methodology will be biased to those liable to undertake distracting activities or be distracted. Furthermore, perhaps some would not even partake in the study because it's a distraction relative to why they're in the class in the first place.
Not saying that is demonstrable or true. Don't downvote the hypothetical messenger and all :p
And yes, I'd expect weaker students to be the more likely to spend their time / privacy on extra points.
Finally, doing slightly worse on two hour gen eds is also not the same thing as doing worse in general. Those classes are ones students are forced to take, often with professors who are forced to teach them. I know my gen eds were lower quality classes, with more people, less participation, worse teaching, and worse assignments.