Yes, there are two independent probabilities combining, which is a multiplicative effect. A competent assessment should take that into account, or at least say that the results are inconclusive due to not having enough data. So a good professional assessment would do that, but journalists or unprofessional people might easily mis-read statistics. Math: For example, if in environment A, the chance of getting sick from COVID in a certain period of time is A, and if in environment B, the chance of getting sick from it in the same period of time is B, and the chance that a vaccine will prevent COVID sickness is V, then the chance of someone with the vaccine getting sick from COVID in area A is proportional to A / V, and the chance of them getting infected in area B is B / V. That is, if the chance of an UN-vaccinated person getting sick from COVID in area A is X times as high as in area B, then the vaccinated person would also have X times greater chance of getting sick from COVID in A than THEY would in B. I.e. It is not meaningful to say what an effectiveness rate is, without saying what the context is. In the above, the rate V would be the rate of effectiveness for someone being deliberately exposed to ha very high amount of contagious COVID virus. If looking at actual infection rates for vaccinated people, their environment absolutely does need to be taken into account. After all, if you assessed the effectiveness of drinking 7-UP on subjects in Australia during a period where no one there caught COVID, you’d see 0% infections. There are some statistical details about vaccine effects that I don’t know that might somewhat affect how that works, but that’s the basic gist of it.