Is it possible to prevent the capture of report run history?
I want to force the report to execute whenever the user clicks on the name or the 'run' button and never capture any output versions/history.
I tried removing Write access to the folder for the user but still the output was captured.
If your goal is to always run the report, look in the properties for the report on the "Report" tab. Change the default action from "View most recent report" to "Run the report".
I believe run histories are only kept for scheduled items. I am pretty sure you cannot eliminate that, though you can limit it in the report properties. You could remove their capability to set up schedules altogether, if that is the core issue. I have not had my morning dose of caffeinated beverage just yet, so I may be missing your actual goal.