Well, I haven't read most of the thread, so I dunno everything that's developed since. So, here's my take from it:
Telling us the lead-in story about the 'problem player' who's always engrossed with his phone definitely struck me as an effort to provide "justifying background" for what you chose to do here. While that's neither here nor there for whether you were wrong or not, it communicates some perception that your actions did need to be justified.
I don't think it was wise to avoid letting people know what was or wasn't magical. Identifying items is quite easy in 5e (not quite as easy as 4e, but close). While it may seem like an opportunity to you, that kind of uncertainty hanging over a party's heads can already be a sore spot. That is, for players who aren't completely on board with it, it can feel like adding a new onerous task after having already completed a major objective; "we won the fight, why make us wait to reap the spoils?!" kind of thing. There are definitely players that don't mind that at all, and players that like it a lot, but I think the shift towards more easily-identified, quickly-employed items is an important paradigm shift in the D&D (& related games) community that shouldn't be opposed lightly.
I think you did do your Ranger's player a disservice by failing to explain what "the full set" meant. While the player might have forgotten, the character almost certainly would not have. They all clearly noticed the ring fixed on the finger, you made sure of that, so it would be the pinnacle of foolish, self-detrimental behavior for the Ranger (character) to forget something they had specifically earmarked as important. I am generally quite able to maintain attention in a game (my bigger problem is usually that I have too much room, so I look for other, little things to do to fill up time while I keep track of what others are doing), but I can be very absent-minded. It's possible--not likely, but possible--that I could have made a similar mistake, and I would certainly feel upset if you had done this to me.
It was an interesting idea to turn the unfortunate situation into a plot opportunity, but it might have been better to take a slightly different tack. E.g. the blacksmith admits that he cheated the Ranger out of the true worth of the item, but isn't quite willing to just hand it back over since it was a legitimate, agreed-upon deal. So, instead, he offers an exchange: "Bring me something I could work into a masterpiece of my own, and I'll let you have it back, with the money in exchange." That turns the fiasco into an outward-facing, potentially plot-generating quest, rather than an inward-facing, how-dare-you-cheat-me situation.
So, in short: I think you made an potentially-unwise, but understandable, move in making the items difficult to identify; I think it was an unwise move to do nothing more than ask about "the whole set" without being any more specific than that (since, as others have said, "set" is often used just for an "individual" equipment item, e.g. "set of full plate" even though that doesn't typically include gloves, boots, helm, etc.); and I think that while it was a good thing to make it a plot opportunity, your specific execution of it (from what was said in the OP) left something to be desired. That the allegedly "culpable" player has issues with being distracted during your games neither justifies nor mitigates this.
Or, if you really want it short: You set the group up for a fall, and then got surprised when they were upset at being set up so. Blaming cell-phone guy for misunderstanding your intentionally vague terms pushes it over the line in my book.