That made me try to find the remission rate of Hodgkins Lymphoma, and according to this 2005 paper [0] it is indeed very rare, the paper says that only 15 cases have been recorded. The interesting part: The patient in that paper had "complete remission during intensified care for interstitial pneumonia".
Fever may be an important factor. IIRC statistically people who had one severe fever in their life, have a lower incidence of cancer.
I think the double edged blade here is not the anti-viral response, but autoimmune reactions, which are excerbrated by tissue destruction and an overall activated immune system.
Cancer needs to gain immune cloaking and a viral infection may present the misbehaving cells by chance.
[0] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2815821/