Maybe try reading the studies they cited and linked? https://www.sciencedirect.com/science/article/pii/S266637912...

> In the first transfer experiment, most patient participants had been vaccinated prior to sampling, whereas the controls were not. Importantly, in our follow-up experiment, we used post-pandemic controls (exposed and vaccinated), and their IgG still did not induce the overt pain phenotype seen with long COVID IgG, suggesting vaccination alone is unlikely to explain the transfer effects.