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.

“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.”

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.

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

That's interesting. I wonder if most of the unvaccinated population has already been infected with an older variant of covid-19, and if that previous infection provides a more effective immune response than the vaccine for omicron?

You cut the sentence in the middle: "though individuals who had received at least one dose of a COVID-19 vaccine continued to be less likely to test positive for COVID-19, regardless of variant." Which does not mean the unvaccinated are more likely to get omicron like you originally claimed. Just that if they are infected it is more likely to be omicron. Which means the vaccine is less effective against omicron than other variants, which we already know.

You’re misinterpreting (unintentionally or otherwise) this statement.

All this is saying is that P(Omicron variant | positive test AND 3x vaccine) > P(Omicron variant | positive test AND no vaccine).

In no way this is implying P(Getting Omicron | 3x vaccine) > P(Getting Omicron | no vaccine).

That... Is a different statement. It says that they are more likely to have a specific variant, given that they got infected. It did not say they are more likely to get infected. Right?

When you are given priors you have to be very careful about what answer you are getting actually says. It says there are different viral profile in one group vs the other when we explicitly select for people with virus. Doesn't really tell us the detail involved of actually getting the virus.

Feels like that’s more a statement about the efficacy of the vaccine against Delta vs Omicron. “…and test positive for COVID-19…” already narrows the groups down to only the positive cases, it’s not a statement about those groups’ relative sizes.

That para makes 2 more important points:

"Vaccination status: those who have received three doses of a vaccine and test positive for COVID-19 are more likely to be infected with infections compatible with the Omicron variant compared with those who are unvaccinated, though individuals who had received at least one dose of a COVID-19 vaccine continued to be less likely to test positive for COVID-19, regardless of variant. It is too early to draw conclusions from our data on the effectiveness of vaccines against the Omicron variant."

“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.”

And when was it censored?

I note that it says "It is too early to draw conclusions from our data on the effectiveness of vaccines against the Omicron variant." also.

Does it mean more likely to get infected (given the same exposure) or more likely to be infected? The difference is quite important.