No, they don't deliberately omit the part of the quote. They are either unaware of that part of the quote or don't think it matters to the point they are making.
Yes, if you quote Knuth here (whether the short quote or a longer version) you are probably responding to someone whom you believe is engaged in premature optimization.
It remains that the person quoting Knuth isn't claiming that there isn't such a thing as justified optimization. As such, pointing to the context doesn't really add to the conversation. (Nor does a thoughtless quote of Knuth either)
I dunno, guess it's hard to say given we're talking about our own subjective experiences. I completely believe there are people who just know the "premature optimization is the root of all evil" part and love to use it because quoting Knuth makes them sound smart. And I'm sure there are also people know it all and who quote that part in isolation (and in good faith) because they want to emphasise that they believe you're jumping the gun on optimization.
But either way I think the original statement is so uncontroversial and common-sense I actually think it doesn't help any argument unless you're talking to an absolutely clueless dunce or unless you're dealing with someone who somehow believes every optimization is premature.
Yes, if you quote Knuth here (whether the short quote or a longer version) you are probably responding to someone whom you believe is engaged in premature optimization.
It remains that the person quoting Knuth isn't claiming that there isn't such a thing as justified optimization. As such, pointing to the context doesn't really add to the conversation. (Nor does a thoughtless quote of Knuth either)