Sure but the point is that vaccines are supposed to make it less likely for people to test positive at all.

The numbers given of 62% of the population vaccinated in Israel vs 82% of new cases being vaccinated means the vaccinated are more likely to test positive vs just positive cases are more likely to be vaccinated.

I'm sure they just have their numbers wrong, though. The article is just badly written in general.

For example:

It stands to reason, therefore, that new cases are >more likely to occur in vaccinated communities >as they make up more of the population.

This is not right.

What they are trying to explain is that new cases are more likely to come from vaccinated communities whilst still being less likely to occur in vaccinated communities since vaccines have efficacy all others thing being equal.

I think the writer of the article was trying to explain a concept without being careful with the concept themselves.