It sounds like a problem not so common in western Europe, but it was when I was a fresh student (around 1994). The Radboud's University Library certainly did not have all journals and for one journal I had to go to a research department and sit in their coffee room. Not a problem at all. Big Package deals improved access, but created a vendor lock-in. And we're paying Big Time for these deals now, with insane year-over-year inflation of the prices.
But even then, I was repeatedly confronted with not having access to literature I wanted to read. Not just me, btw, for PhD students this was very common too. In fact, they regularly visited other universities, just to make some copies there. An article basically costed a PhD a train travel and a euro or two copying cost (besides the package deal cost for the visited university, of course). Nothing much has changed, despite the fact that in this electronic age the cost should have gone down significantly, instead of up.
That Elsevier sues Sci-Hub (about Sci-Hub, see this and this), I can understand. It's good to have a court decide what is more important: Elsevier's profit or the human right of access to literature (doi:10.1038/nature.2017.22196). This is extremely important: how does our society want to continue: do we want a fact-based society, where dissemination of knowledge is essential; or, do we want a society where power and money decides who benefits from knowledge.
But the STM industry claiming that Sci-Hub does not contribute to the scholarly community is plain outright FUD. In fact, it's outright lies. The fact that Nature does not call out those lies in their write up is very disappointing, indeed.
I do not know if it is the ultimate solution, but I strongly believe in a knowledge dissemination system where knowledge can be freely read, modified, and redistributed. Whether Open Science, or gold Open Access.
Therefore, I am proud to be one of the 10 Open Access proponents at Maastricht University. And a huge thank you to our library to keep pushing Open Access in Maastricht.