I dont really appreciate the conspiratorial or political framing, but I will contend that these results seem to support your claim.

It’s ironic that the article is about people using the study to spread misinformation about the results of the study.

Social media users are misrepresenting these findings (on Omicron’s apparent ability to breakthrough vaccine protection) by saying those vaccinated are more susceptible to infection overall.

“Note that this is the probability of an infection being Omicron given a person is infected, so it doesn’t tell us how likely a person is to test positive in the first place.”

Did you read the whole article you linked? It doesn't say the vaccinated get Covid more often than unvaccinated. (They don't.) It doesn't say the vaccinated get Omicron more than unvaccinated. (They don't.)

It merely says the vaccinated are infected by Omicron more than other variants like Delta. That's it. In other words, the vaccines are quite effective against Delta, but due to mutation, Omicron can slip past immunity a little easier.

The vast majority of folks in hospitals and the morgues from Covid (Alpha, Delta, or Omicron) nowadays are unvaccinated.