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Alt rock at the time was simply rock that was divergent from the hair metal that was popular then. It's not really much more complicated than that. A few of the alt-rock bands (early AIC and Soundgarden, Temple of the Dog a little bit) even have some remnants of that style that you can hear in their work. Soundgarden's "Searching With my Good Eyes Closed" edges right up to the line of hair metal, "Say Hello To Heaven" by Temple of the Dog, a lot of AIC songs do as well. So some bands sort of grew into alt-rock out of the more hair-metal stuff, and some like PJ and Nirvana started out already divergent.
I don't disagree with your observations about how it was labeled at that time but you're illustrating my point. Through mid-1991, "alternative" referred a wide range of music that was technically best described as rock, but nothing like mainstream rock on radio and MTV (which, with a few exceptions, was mainly hair bands). It included sub-genres of 'college radio' and even some remnants of punk in the US, some more ethereal/emo/goth stuff mainly coming from the UK, and a whole sub-genre of electronic-based rock.
Pixies, Sonic Youth, Jane's Addiction, Stone Roses . . . those were the sort of standard-bearers of "alternative rock" before the grunge/Seattle thing started hitting in late '91. And some the 90s most noteworthy bands were genuinely alt-rock but aren't grunge by any means (Radiohead, Pavement, Ween, etc.).
I think if you look at lists by competent publications (Pitchfork, Rolling Stone, Consequence of Sound) of the best albums of the 90s, or even the best alternative albums of the 90s, Nevermind is the only Seattle/grunge album in the top 10. I'm not saying that's gospel or that it must be accepted - those lists are obviously highly subjective. I'm only saying that I take issue with people using "alt-rock" and grunge co-extensively without acknowledging that alt-rock is a much wider net than that, and most of the really noteworthy alt-rock wasn't made by Seattle/grunge bands.