The opening to the actual paper is quite explicit that (i) other studies have already tested commercial apps with with unimpressive results and (ii) a popular open source app for carb counting directly relies on API calls from these frontier models, and this research batch tested the images used the exact same models and prompts as the popular open source app.
So it would be more accurate to test the apps rather than the APIs, unless the goal is to warn people that just open chatgpt and ask there.
(And of course it would also be far more tedious to submit each picture 500 times manually using an app and manually log the response than using a script which is designed to collect the data automatically as fast as API rate limits permit)
This is all in the first few paragraphs of a preprint paper describing the research in considerably more detail which is linked at the bottom of TFA
Meta: enjoying nearly half this HN thread being arguments that surely people care about what's in their food don't ask ChatGPT for comment instead of looking it up properly, and most of the rest of it being people who apparently care what's in a research paper asking HN for comment instead of looking it up :)