I don't have time to do a serious search but here's one:
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=12208187&query_hl=3&itool=pubmed_DocSum
It's entirely possible that it promotes some types of cancers (i.e. of the upper digestive tract) and inhibits others (after it is partially digested into different compounds by the high acidity of the stomach and/or by the liver). Aspirin is like that -- preventive effect on colon cancer, but promotes pancreatic cancer (it's generally recommended because colon cancer is far more common than pancreatic cancer, but people with a family history or other risk factors for pancreatic cancers are being advised that it could have a bad net effect on their risk of either cancer).
The capsicum family includes a variety of plants, including sweet peppers, which produce different capsaicinoid compounds which have different effects (I don't think research is very advanced on any of them, but I'm sure that's about to change re capsaicin at least). It's entirely possible that most have only a beneficial effect, and that capsaicin quickly converts into something more like the others (i.e. losing the feature which causes the burning effect while retaining other beneficial features).
This link is to an abstract re capsiate, a non-burning capsaicinoid found in sweet peppers, and its anti-cancer properties.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=12594536&query_hl=7&itool=pubmed_docsum
CONCLUSIONS: These results suggest that capsiates and related synthetic analogues target a variety of pathways involved in cancer development and inflammation, and have considerable potential for dietary health benefits as well as for pharmaceutical development.