Dead wrong; you've misunderstood how evolution works.
As the population of prey reduced, the fecundity and population size of the new stronger humans would fall, but the fecundity of their weaker rivals would fall even faster. As the human population crashed, the trait would gain ground, becoming present in a greater proportion of the survivors. Eventually, the human population would likely stabilise at a lower level that the prey could support, as the weaker humans died out.
A relatively superior trait could drive a population level down to extinction in the absence of a counter-balance, but an improving predator/prey ratio provides such a counter-balance. We can expect this process to have occurred as we grew in intelligence.
Evolution in sexually reproducing selects for the fittest traits/alleles relative to rival traits, even at the expense of the fitness of the host species to its environment.
To illustrate how deadly evolution can be for a species, consider what might happen to the human race if a male developed a mutation on his Y chromosome that suppressed the production of sperm with X chromosomes, so that all his kids were male...