I think this takes an overly-simplitisic view of APIs. Going by the primary example in the article, by representing a pet's owner as a link instead of an id, they're basically discounting the idea that there may be separate endpoints that take in an owner id. For example, if there was an endpoint that let you get the invoices by customer, you would still need to understand the templates for that endpoint.

More fundamentally, I think it's trying to solve a smaller problem in the face of a much bigger one, you still need to know what the response of any given endpoint is going to be. Just because they've passed me a link, doesn't me I don't need documentation on what endpoint that link points to. I still need to know that the owner is a link to the people endpoint so I can properly parse that result. That in turn requires just as much documentation (IMO) to describe the relationships as it would to properly document your URI templates.

Obviously, the primary reason to use links over ids is to give the developers of the API more control over changing things like routes and Ids and whatnot, but I feel like it is a bit disingenuous to make it out to be a much better user experience or something, since it really isn't.