How troubled one is by this essential solitude depends on how much one is troubled by ordinary aloneness of course. I'm an introvert and recharge by alone time (though I value social contacts too).
The quote has a point: getting killed or having sex are not the best ways to overcome loneliness.
But my ‘imagining’ of your mental state, and my ‘knowing’ of my own are both guesses.
I love how you draw attention to this similarity. It sounds and feels similar to some meditation experiences I had.
There is still a quantitative difference. The access to one's own feelings and mental states is more direct. But you still dissolved the quantitative difference into a qualitative one.
A quote from Aldous Huxley that has stuck in my mind more than perhaps any other over the years:
I used to be fairly troubled by this kind of thought. These days I’m more inclined to think of memories of myself, my own writing from yesterday, my sense of a person in my arms, words vibrating my inner ears as light bounces between someone’s eyes and mine, words reaching me across the internet from a stranger, barely understandable lines from thousand year old pages, as more of a piece—physical communications between scattered consciousness. All interpreted with more or less insight and confidence and detail and sense of being an ‘experience’ and not just ‘information’, depending on the quality and nature of the message. But my ‘imagining’ of your mental state, and my ‘knowing’ of my own are both guesses. The sense that they are different is a pragmatic, superficial, quantitative one, not the symptom of a deep metaphysical separation.