Um, my dictionary says capsicum (> capsaicin) might be from capsa, i.e. because the pepper is in a case or capsule.

Hm, Perseus Lewis & Short doesn't list capsa -- must be Late Latin -- they have capsus (i) wagon-body or coach-body, or (ii) pen, enclosure; and capsella a small box or coffer.

I just thought the caps- idea was possible, because breaking down capsids could well be akin to whatever is needed to break up cells in apoptosis.