It is possible to have the time stamp dropped if going to some other formats. It would take tools that the husband would not have, or probably not even know about, to strip the time stamp from the original video format and keep that same video format. The cops, would want to have the original source video to look for stuff like this.
What I'm waiting for is for someone to come back with another theory about the video.
Does it matter at all what type of camera it was recorded on? I suppose if one entered zeros for time or used a date of 1/1/01 or similar when new then there would be no valid time stamp at all?