I view this in a sort of "alone in a crowded room" way whenever I hear something like it.
Surely you can be surrounded by people- strangers, friends, family, etc. However, you are the only person in your own head-space from birth until death. You are the only one to be in your world in the precise way that it is your world, and no one can ever truly meld with it exactly as you do.
Typically, the isolating part of quotes like these is the bit where people put so much stock into what they are surrounded with that they forget to become well-acquainted with themselves. It's a lonely time when you are not on your side, when you may not even know your side at all. How can anyone ever really properly integrate if we're all so far outside of ourselves? So, perhaps, when it comes times to die we can really be that devoid of another soul- even our own.