Of course it's true, that it's far more important to have photographer skills (find a good motive, angle, frame it right, lightning, etc.). That's something you can't buy though. Also he doesn't really shine in this regard, to be honest.
BUT, to support his point (and my last one), take a look at this: http://mostlylisa.com/worldtrip/ So again, it's the photographer and his skills and not the technical details. You'll quickly hit limits with a smartphone though (as you described in your post).
edit: Also, the main blog will show pictures taken with a full frame DSLR which simply wouldn't be possible with a smartphone. http://mostlylisa.com/
Yikes! Kind of harsh, don't you think? (I am not the author.)
I've been there--a few years ago--with a point and shoot camera, taking what I thought were better photos than the pros. If I'd gotten a DSLR at that time, I wouldn't know what to do with it. But as I got more and more interested in photography, I started to understand the complexity and limitations, and moved up to a DSLR. Yes, I started on Auto mode and as I learned more features I used them more.
Yes, the lines between photographic technology are blurring. I've taken some incredible photos with my Note II (same phone as him, and far better quality than his), but I've also been extremely limited in many situations. He's only taking wide angle still scenes, which doesn't take much skill or technical ability. There are far more situations in which a cellphone can't even compare.
He says "Why burden yourself with such a bulky device, not to mention the cost of it, when your good old phone can take just as good photos." In reality, the Note II cost more than my DSLR ($700 vs $600), and the bulk of it is not just for ergonomics but also to keep it steady and shake-free.
Lastly, and this is the part I hate to be a jerk about, but the author is probably right, at least for himself right now. I don't think he'd stand to gain all that much from a higher-end camera today. With practice, though, further developing a critical eye, and understanding the photographic process, in time, he might be well-served by upgrading.