Why would this be a security issue? I'd like to hear the explanation for the security issue.
As the server creates a small video file of the last few minutes anyway, it has already been rendered/created so there is no further action required from the server, apart from providing this rendered/created video file to be downloaded. With a bit of communication, it could also be enhanced by downloading the rendered/created video file straight away onto the users computer automatically. For users with high end pc's or for the ones who use their own video capturing software anyway, they could implement a new tick box in the settings, so that these users can turn off the function of automatically downloading the video file from the server.
It's no rocket science to program this at all and shouldn't also take too long to implement this feature.
Regarding who's job it is, this is quite debatable in my opinion. Why you might ask. Well if TruckersMP saves a video file upon reporting someone ingame anyway, why not provide the user who reported the other player, with the evidence created by the server. There may be a demo system but what purpose does it serve the user, if the report has not been claimed for 10 minutes. If it is being stored even after it timed out, it'd be nice to at least get the report number, so that if you have to report the player via the web reporting system, you could add the ingame report number.
As this may take more time for the supporter/admin who deals with that report, the idea of downloading the demo/video file is the easiest as this could be attached to the web report and the supporter/admin has to view only this report.