There was just an emergency call regarding a corrupt MP4 clip saved from an ultrasonic device onto a USB stick, presumably containing first recordings of the reporter's offspring. The file contained the MP4 container header, but missed the content stream headers which were probably truncated at the end of the file.
Searching in Google with a last bit of hope, and obviously a good bit of luck, I discovered the following tool:
recover_mp4 or as online service:
http://restore.media/
It attempts to extract headers from a known-good spare clip and to apply them to the corrupt clip. Several video cameras are specifically supported, and there are numerous advanced parameters to control its behaviour. The author even offers supporting a restoration with his own experience.