You're right. I mean technically it gets copied at some point, more by them than by you. But we can't really go down to what's happening technically because then almost everything involves copying content... It's just how computers work. Even watching Netflix requires your device to copy around the stuff internally. And we're having issues with that. For example illegal images ending up in the browser cache. The browser needs to hold on to things intermittently and then you're in possession of them even if you never really saw (or saved) them... And there are lots of similar things with copyright and copying. And if we can't look at what's actually happening, what then are we judging things by?

In the end every "DVD" or "lending" analogy breaks at some point. With law everything depends on the exact jurisdiction plus the exact circumstances of that case, anyways. So the correct answer will be "It depends." nearly every time. But also copyright law wasn't made for this. It's from a different time. And it'd need a complete overhaul to address the real world as it is today. But instead, it mostly got amended and revised incrementally.
If your law addresses sharing content with friends... That's the proper way out of the debacle. Now it also needs to factor in the two cases that you could share something that you yourself obtained from a legal or not legal source. And we'd have a proper answer to the initial question.

In my opinion the practical questions are different anyways: Is that friend going to rat you out? Are they going to share the credentials to your library with other people? Or brag to their friends about not paying for streaming anymore and having access to a 30TB Jellyfin library? Because if word spreads, you're bound to get in trouble. (And you'll have to deal with other people wanting access...) If they keep it a secret... Nobody will know, so there also won't be any additional consequences attached to it. Apart from you already downloading and saving the stuff...