I am sure Paul can and will answer for himself but...

"what does this formulation mean, e.g. — "I'd argue that all humans are closer than humans to all animals, but most animals are, in the big view, pretty close to us too.""

I took that to mean that as humans we all have far more in common than we don't but as animals we are all pretty much close to what other animals do. I could be wrong but that was my interpretation. If I am right then it does make sense on a behavioural, genetic and evolutionary level for sure.

mp