SARS-CoV infection can produce IgG and neutralizing antibodies that remain detectable for months, and some SARS-CoV antibodies have cross-neutralized SARS-CoV-2 in vitro. However, laboratory cross-neutralization does not establish preexisting population immunity or durable protection after SARS-CoV-2 infection. Differences in the spike receptor-binding region and ACE2-interacting residues may limit cross-protection, so SARS-CoV antibody evidence should not be treated as proof of immunity to SARS-CoV-2.