I'm inclined to agree with this... mostly. I grew up in a very rural part of America (graduated high school with a couple dozen other kids) and now live in NYC. College was by far the best place for me socially so far in life. So I think it's pretty critical to find that "third place" where you can rack up 40 hours of friendship to get close with someone.
School where I grew up wasn't much better than homeschooling sounds for the grandfather comment here: there just wasn't a culture of academic interest or many extracurriculars that interested me, beyond musicals and a school quiz team. Awkward high school me just didn't have much in common with the majority of kids where I grew up. A couple dozen classmates really isn't much to choose from. So I think you're overlooking the fact that you need a base of at least enough people that you can find some folks with similar interests, or at least people with compatible personalities.
Community college was a positive leap because I had a lot more diversity of classmates from all the different classes I took. That was the first time I was a member of a population large enough to actually find like minds and clubs/activities where I could build relationships.
Four year college was the best: I had friends in almost every class, most of the dorms, and had activities like TAing that actually interested me. Thousands of other similarly-smart kids with hundreds of clubs and activities to meet people? That's a perfect formula, and I wish I could replicate it in the post-graduate world.
Living in NYC since graduation has been a mixed bag. I feel like most people already have established friend networks so you need at least one decent connection to make it into one of those networks. One difficulty I found was that it takes a lot more active effort to maintain friendships. My college friends do not live nearby, so I have to organize travel to see any of them or at least try to call them up every week or two.
The other struggle is that most folks just don't have that much time outside of work. When I add up work (8-10 hours a day, including commute), sleep (6-8 hours a day), running (1 hour a day), cooking (1-3 hours a day)... there's only a couple of hours left to do anything. If you need to travel more than 30 minutes via subway to meet up with a friend, it's easy to start cutting into sleep time. God help you if you have a kid, or a dog, or a significant other who gobbles up more of that time.
Anyway, that basically means that most of my friend-making in NYC has boiled down to "people I work with" because that's the place where I see the most people other than my family/existing friends the most consistently. If you're not at a company with a culture perfectly aligned with your personality, it can be tough to make friends at work, and then you get isolated pretty easily.
I still haven't found quite the right formula for friends here: I've participated in running clubs, gyms, book clubs, and volunteer work, and none of them have hit the right balance for "regular group interaction" and "people I mesh with well." Hanging out at bars and coffee shops has its place too, but gets pricy and can be lonely to do alone at first.
All in all I think the big city just feels more isolating if you don't have friends because it seems like everyone else already has friends here. When I lived in rural America, it was depressing because I knew there was nobody I even wanted to hang out with. In the city I at least have hope that if I meet the right people -- who are definitely around here somewhere -- I could establish a great group of friends. The trouble, as it always is, is in meeting them.