This claim is totally false for cochlear implants. I am a cochlear implant recipient and before the implant I had essentially no hearing in my right ear ("profoundly deaf"). With the implant in my right ear my hearing has been restored to 90%+ of normal hearing.
I did a whole raft of audiology tests and for the speech comprehension tests in particular I scored 90%+ compared to people with normal hearing. (They're tough tests too, trying to pick out a sentence from a lot of background noise which is a worst-case scenario for hard of hearing people.)
I was told that my outcome was better than average, but I was a younger than average adult recipient given than I was in my early 40's, compared to most (in Australia at least) who are 60+.
And yes I can now distinguish all notes on a piano.
I don't think any of this is particularly relevant to understanding spoken language, but I'm just curious about your outcome.
I'd be surprised if a majority of current CI users could distinguish e.g. middle C from C# (not identify the note, but just perceive a difference between them), but I don't know that many CI users.
Note though that I had perfectly normal hearing until my late 30s, and only have an implant in one ear. After my implant operation my brain "knew" what it should be hearing from the implant signal. This is apparently true of many adult CI recipients and the unexpected plasticity of adult brains to adjust to the CI signal is an active area of research.
I think that the typical outcomes for people who have cochlear implants when they are born deaf would be quite different to adult recipients like me who grew up with normal hearing.