Those are basically the city core neighbourhoods. Seattle city limits stretch rather far north into neighbourhoods like Ravenna and Phinney Ridge. I am not sure which neighbourhood the person you are replying to is in, but their story doesn't sound unbelievable outside of Capitol Hill plus the "core" neighborhoods you mentioned.
That makes sense.
I’d guess if we define city living as an affluent neighborhood within city limits that one can live/work/play in without getting in a vehicle there are areas that fit the bill in nearly every city assuming that one has the correct income and profession to slot into it.
Seattle is a city of neighborhoods. Move a few block away and the experience would be completely different.
With that said, you visited what I would consider some of the worst places in the city to spend time with kids.
I will say as far as cities go those effected with homelessness were not as aggressive towards me/us as I’ve experienced in other cities, but they were extremely aggressive towards each other and didn’t make it feel like a very welcoming place for families.
Perhaps the few days my family was there gave me an inaccurate impression. I’ve been there numerous times for business and always enjoyed the city, but those times tended to involve a lot more Lyft rides and eating/drinking at higher price point restaurants than walking around exploring the city and time in the parks. With my family we were mostly in the First Hill, Downtown, Pioneer Square, and a bit in Belltown neighborhoods.