ABSTRACT - Many media and public-record statements, including Congressional statements and testimony, since 2022, have often asserted that COVID‑19 vaccination in the USA prevented some 100 million infections, saved some millions of lives, saved some tens of millions of hospitalizations, and saved some 1 trillion dollars in associated medical costs. These fantastic and unverifiable claims are based on theoretical models of so‑called counterfactual scenarios, which are back predictions under hypothetical absence of COVID‑19 vaccination. The said claims are reported in several scientific articles, often in leading scientific journals, however their authors sparingly show and essentially never examine the time evolution of the back predictions for plausibility. We calculate time evolutions corresponding to the back predictions. We show that if one accepts the counterfactual models and their inputs to then calculate the corresponding excess all-cause mortality that would have occurred, then one graphically obtains excess all-cause mortality by time (by week) that is contrary to realistic behaviours. By accepting the counterfactual models, we must believe that the two main COVID-19 vaccination campaigns (doses 1+2 and first-booster dose rollouts, in early and late 2021, respectively) coincidentally were each applied just in time prior to two staggering spontaneous many-fold increases in viral virulence. In other words, we must believe that the massive and repeated COVID-19 vaccine rollouts did not significantly reduce mortality in 2021 and in 2022 compared to 2020 (they actually did not) because the virus became more virulent than ever in those years, twice, in early 2021 and in late 2021―early 2022, producing 5‑fold hypothetical increases in excess all-cause mortality by year. The counterfactual scenarios are so improbable that they can, on the sole basis of the predictions themselves, be qualified as impossible.