This doesn't make a lot of sense to me, and it doesn't seem to be backed by any evidence, either in the original Twitter thread nor the linked blog post.
I think far more likely what's happening is Pinterest is actively crawling the web for images and surrounding text. They will then perform their own reverse image search on _their own_ database, and add this context text to their existing copy of the image, or create a new one if one is not present.
Why would they rely on a user submitting a picture then go to the trouble of reverse searching it? I think they are much more proactive than that.
A lot of business accounts sign up to activate Rich Pins which adds a few additional features when people pin from you site.
When you are signed up for this they will scrape the page the pinned image comes from to collect some extra info on the page to show along with the pin.
I’m not sure how if they do this if you are not signed up for Rich Pins though.