First, there are some studies, i.e. tinyurl.com/y8zzf8tw, that show a cross-reactive T-cell response in sample taken before the pandemic, due to previous infection with common cold coronaviruses.
Second, it has been descriped that people exposed to SARS-CoV-2 only mount a T-cell response but do not produce any antibodies. From this, some people like to conclude that