quite actually means completely, or to an extreme. So you could say "She was quite right about blah blah blah" and it would be the same as saying "she was completely right about blah blah blah"
It had the same British definition initially, which is why if you ask a British person "did you like X" if they still respond with "Quite." They mean yes, they did like it. The definition changed for British (Although any dictionary will still show the true meaning) because it started off as a kind of sarcasm, "Oh she's quite the beauty" to an ugly person, but eventually people didn't realize they were being sarcastic and started using it as a serious expression.
It had the same British definition initially, which is why if you ask a British person "did you like X" if they still respond with "Quite." They mean yes, they did like it. The definition changed for British (Although any dictionary will still show the true meaning) because it started off as a kind of sarcasm, "Oh she's quite the beauty" to an ugly person, but eventually people didn't realize they were being sarcastic and started using it as a serious expression.