It appears to come from a researcher contacted by the site for the article. And it's probably true.

However, there's a few reasons to believe that "long" covid like symptoms wouldn't come from the spike protein alone:

1. As a parent mentioned, you generate a lot fewer proteins w/ the vaccine than the virus

2. IIUC, those proteins are more localized. The soreness with an initial injection is inflammation due to spike protein creation, and that's usually localized to the injection site. The proteins themselves are less likely to travel as widely as the virus.

3. The proteins don't last very long. They're gone after a few days. So long term symptoms wouldn't be due to a continued immune response. They might be due to inflammation that hasn't gone down, I guess, but that seems unlikely to last months.

And again, all of these will be worse with the virus than the vaccine. You'll have more spike proteins, for longer, over a larger part of your body, and also have a virus attacking you in addition to the immune response.