Does capsaicin in food kill bacteria?
In 2014, a review article was pushlished by the Department of Food Science and Nutrition at the University of Minnesota-Twin Cities, one that outlines  studies that (collectively) target the top 14 food-borne pathogens in attempts to identifying any potential antimicrobial properties of chili peppers, given that chili peppers can contain high amounts of capsaicin. 

From the abstract of the article:


  Chili peppers are used worldwide in foods for their pungent flavor, aroma, and to prolong food spoilage. With capsaicin contents ranging from zero to millions of Scoville heat units, the different varieties offer a wide range of options for people all over the world. In addition to their use in cuisines, chili peppers have been explored for their antimicrobial and antifungal properties. 


.. 


  This review goes over some relevant research that has already been done in this area. In addition it lays the ground for the new research that is emerging testing new varieties of chili peppers for nutrient content, flavor profiles, and for antimicrobial activities against numerous human pathogens.



The fourteen pathogens that were targeted and tested against were chosen due to their high risk of harm to the general public, most especially pregnant women (according to the FDA). To name a few that are well known, there's: Clostridium botulinum; Escherichia coli; Salmonella (enteritidis and typhimurium); Staphylococcus aureus; and Listeria monocytogenes.


After reading the conclusions of several studies that were provided by the review article (as well as the conclusion of the review article itself), it would seem that the current (as of 2014) consensus is that the efficacy of capsaicin (in chili peppers) as an antimicrobial agent is still to be determined. Of the (multiple) studies that were considered, collectively they produced quite mixed results. The reason for this is because each study has their own method for testing the antimicrobial activities of capsaicin, which makes the comparison of results between tests difficult to perform with confidence.


  There are a variety of methods for testing the antimicrobial activities of chili peppers. These methods strongly affect the observed levels of inhibition. Various reasons may contribute in the differences between results, including inconsistency between analyzed plant materials.


..


  In these experiments, crude extracts of chili peppers were used; no
  separation of pepper components was done. Based on the data, it seems that capsaicin had a lesser antimicrobial effect compared to other components of chili pepper extracts. Therefore, future studies should try to determine what compounds in the chili pepper gives the spice its antimicrobial properties, and to do so purification of the extracts is necessary. Capsaicin gives chili peppers the ‘hot’ sensation, which some people might not like. It would, therefore, be beneficial if there is another substance in the pepper that could be used in the food industry as a preservative without the pungent taste and hotness.


So, it would seem that, since the idea of using capsaicin as an antimicrobial agent is (fairly) new, there hasn't been a defined method for testing, and because of that, definitive conclusions aren't able to be made yet.