The first example is not really apples to apples as it doesn't even have error handling which makes the native function look longer. Probably because getJson doesnt support errors by default and you have to use promises http://api.jquery.com/jquery.getjson/
I ran into this issue of jquery silently failing a while ago and will always remember that pain point
I don't think I've ever used getJSON(), only ever the longer form ajax(), and never had issues with error handling, well at least since jquery 1.9 when deferred promises came good. Using .then() to chain events together is very smooth, what I always wanted. I'm lightweight with JS mostly though!
The first time I saw that site, I assumed it was a joke. Seems more to me like it's trying to tell people how nice jQuery is. Who would look at that and walk away with the opinion that jQuery is unnecessary?
The site suggests you try not to make it a dependency if you're writing a JavaScript library. I also suggest vanilla JavaScript for simple pages that need just a smattering of interactivity.