Since he is PS+ subscriber, he has access to the free PS+ version of Driveclub. He added it to his download list, waiting for the next time he'd be online.
Meanwhile he also purchased the disc version of Driveclub. Full of "GREATNESS AWAITS" thoughts, he turned on his PS4 and went online.
As the Driveclub PS+ version was already in his download list, it began to download. While the game was downloading, he wanted to use his disc version and pushed it inside the PlayStation 4's Blu-Ray drive.
It seems that no one actually ever tested if a user would do that. The disc drive of my friend stopped working right away. Ejecting and inserting works fine, but the PS4 won't read any disc anymore.
We guess that this happened because the disc version and the PS+ version share the same TitleID and that having the same one mounted twice is impossible to handle for the PS4. Inserting any disc simply results in a popup, showing that the game is already inserted.
Rebooting the system or anything safe-mode like did not help. Currently his PS4 sits in a service center waiting for a solution.