The whole point of JSON+LD is to make that information more accessible to the outside world (like to search engines), why else would they publish that?

is there any reason to think any site wouldn't want their recipe showing up in a search result?

the 2 sites I talked to were overjoyed to have their recipes shown in my search results.

What copyright? Maybe I'm missing a section but nothing on his site looks like it would fall under copyright protection.

Lists of ingredients aren't protected by copyright. Hell, neither are basic instructions and he doesn't even have those.

Photos are but this looks like it would fall under fair use. If you have a fashion blog you're allowed to use a photo of a dress from the makers website when you're writing about it. It's hard to comment on a product if you can't share a photo of the product. This guy is commenting on various foods by showing their nutritional value.

It's the same way that google discovers them. The JSON+LD is on the recipe page. They place it there for search engines to discover it, so that they appear in a search result with the JSON+LD data: this data enhances the result, instead of just having the name of your recipe, the result contains description, image and ingredient lists.

You can see this in action on google search: type in something like "Chili soup", then it'll return the image, description, some parts of the recipe, etc.