In my experience those people don't even talk about ink, it's all about paper. They must think that you get just a few sheets of paper for a single tree or something like that, when in reality you get like 10 000 sheets of paper for one averagish tree. And those trees are not rare or anything like that, and the process of making paper is nowhere near as bad as electronics industry. Using paper is as ecological as it gets.
With the typical reading volume of an academic and the amount of plastic in my toner cartridges, I'm not sure paper comes out ahead in that comparison.
A high yield toner cartridge can print between 3000 and 8000 pages of text [1]. Average number of pages in a scientific manuscript is 10 [2]. This means that it would take 300 to 800 printed scientific papers to deplete one cartridge. I would have to assume that a single toner cart is not the same amount of waste as a reading device just due to the recyclability of toner carts, but it is up to you how to count them. If I was going to pull a number out of my ass, I would say 10 carts would be equal to one reading device with battery. Let's go low-end and pick 300 papers, which means you would need to print 3000 full scientific manuscripts to equal the waste of one reading device. How many do you read in two years?