This is just an anecdotal experience, but I was living amongst an international coworking community of a few dozen people in South Africa when omicron first broke out, and the vaccination status of people did not seem to have any observable effect on the prevalence or severity of the contracted disease.
That is to say that your sister may have experienced the same effects even if she had taken the booster.
I remember outright lies coming out of the WHO and governments regarding the usefulness of masks (out of a fear of running out of stock for health professionals), and regular exaggerations of the benefit of vaccines coming from politicians (at least in France), where they were drawing a stark black and white picture of a much more nuanced reality.
However, I don't remember seeing false epidemiological data coming out.
Many examples here but “97% of hospital admissions are unvaccinated” was a complete fabrication. Basically they used statistics from when 97% of the population was unvaccinated and kept using them for months longer than they should have. When that wasn’t feasible anymore, they started counting unknown vaccination status as unvaccinated to keep the 97% lie going.
Ironically select ICUs report 90% of their cases are from fully vaccinated now.
We didn't have that kind of discourse here in France AFAIK.
Given that the vaccine is not 100% efficient, past a vaccination rate threshold, it is inevitable to see a majority of hospitalized people being vaccinated.
When the vaccine was first rolled out, official communication was indeed built around P(vaccinated|ICU) but they soon switched to P(ICU|vaccinated) when P(vaccinated) grew high enough to make the first figure misleading.
That is to say that your sister may have experienced the same effects even if she had taken the booster.