Aha! Found it!
This indeed appears to be a Group Policy setting. Specifically, the setting Configure Error Reporting under Computer Configuration\Administrative Templates\Windows Components\Windows Error Reporting\ (this may be a slightly different path, e.g.Administrative Templates\System\Error Reporting, under Windows XP).
This setting contains several suboptions. One is Force queue mode for application errors. The description states:
""Force queue mode for application errors"": Select this option if you do not want users to report errors. When this option is selected, errors are stored in a queue directory, and the next administrator to log on to the computer can send the error reports to Microsoft.
You can change this with the Group Policy Editor. If you are on a domain, you will likely need to change it on a domain controller (I am not familiar with Windows domain administration). For the local computer, launch gpedit.msc (also available under Administrative Tools in the Control Panel) and navigate to the previously mentioned setting.
If you are on a home version of Windows, you will not have access to the Group Policy editor. In that case, you can directly edit the registry key, which appears to beHKLM\Software\Policies\Microsoft\PCHealth\ErrorReporting!ForceQueueMode (source).
There is also a related TechNet article here.