(1) Background: The World Health Organization (WHO) regards atherosclerosis-related myocardial infarction and stroke as the main causes of death in humans. Susceptibility to atherogenesis-associated diseases is caused by single-nucleotide polymorphisms (SNPs). (2) Methods: Using our previously developed public web-service SNP_TATA_Comparator, we estimated statistical significance of the SNP-caused alterations in TATA-binding protein (TBP) binding affinity for 70 bp proximal promoter regions of the human genes clinically associated with diseases syntonic or dystonic with atherogenesis. Additionally, we did the same for several genes related to the maintenance of mitochondrial genome integrity, according to present-day active research aimed at retarding atherogenesis. (3) Results: In dbSNP, we found 1186 SNPs altering such affinity to the same extent as clinical SNP markers do (as estimated). Particularly, clinical SNP marker rs2276109 can prevent autoimmune diseases via reduced TBP affinity for the human MMP12 gene promoter and therefore macrophage elastase deficiency, which is a well-known physiological marker of accelerated atherogenesis that could be retarded nutritionally using dairy fermented by lactobacilli. (4) Conclusions: Our results uncovered SNPs near clinical SNP markers as the basis of neutral drift accelerating atherogenesis and SNPs of genes encoding proteins related to mitochondrial genome integrity and microRNA genes associated with instability of the atherosclerotic plaque as a basis of directional natural selection slowing atherogenesis. Their sum may be stabilizing the natural selection that sets the normal level of atherogenesis.