So, you went with your feelings as opposed to scientific backing on that one. By that rational, they could also be lower too. In fact, they could be on average lower. That statement, however, has some backing. From a vastly larger and more random survey:
https://www.imperial.ac.uk/medicine/research-and-impact/grou...
>The 13th round of the REACT-1 study looked at swab test data from almost 100,000 people in England between 24 June and 12 July. The research found that infections were three times lower in people who were fully vaccinated, compared to unvaccinated people. The data also suggested that people who were fully vaccinated were less likely to pass the virus on to others, due to having a lower viral load on average and therefore shedding less virus.