Interesting - I didn't know that. But the parent was pretty obviously making the association between forms of damage which definitely increase cancer risk (sunburn) and non-ionizing radiation - which does not. The type of burn he observed is thermal.
So even if thermal damage (or just damage in general) can increase cancer risk a little...it's not remotely the same thing as sunburn or gamma radiation, and as it pertains to cellphones completely irrelevant (because a cellphone is not a 40W antenna emitter).
Any time you damage any part of your body, that tissue has to repair itself. There is always a chance (albeit small) of things not repairing themselves correctly and the DNA getting corrupted. Every time the same tissue has to repair itself, the odds of DNA corruption occurring increase. This is why cancer tends to manifest in areas of the body which are chronically damaged and repaired (such as an alcoholic's liver, or the esophagus of someone who has chronic heartburn, or the lungs of someone who smokes).
As such, it stands to reason that any type of burn (causing tissue damage) could ultimately lead to cancer.
One such result: https://www.ncbi.nlm.nih.gov/pubmed/11957286
> Abstract
> Burns are very frequent. Skin cancer on burns scars are one of the known complications....