I'm having a similar problem. First, I took a ton of pictures and videos with the the clock in my camera set incorrectly, now I have a mess. I'm hoping BRU can save the day.
FYI, I think the various "dates" in the EXIF data mean the following:
1) Date Created: All file types seem to have this. For pictures and video, it will probably appear as the date/time you copied it from your camera to the computer. If you copy it somewhere else, it is updated.
2) Date Modified: Updated when you change the file. Rotating a picture for example. For videos, I believe this is roughly equivalent to "Date Taken" in pictures.
3) Date Accessed: I think this is supposed to be update if you look the file, but don't change it. However, if I open a picture in Windows Photo Viewer I would expect it to be updated, but it isn't.
4) Date Taken: Appears to be the date/time a picture is taken. In theory, this should never change (unless the clock in your camera is off). It does not appear that movies have this data field. Some cameras and photo editors/sorting software seem to have a timezone field. I'm not sure if Date Taken is written as "Camera Time +- Timezone Offset" when the file is created, or if Camera Time and Timezone Offset are both written to the .jpg file then interpreted by viewing/editing software.
5) Date: Windows File Explorer lists "Date" in the Details view as default. I believe this is equal to "Date Taken" for pictures and equal to "Date Modified" for videos.
Please correct me if I'm wrong in the above description. I tried to find a good reference to describe it all, but failed so this is just pieced together.
What I think needs to be (hope can be) changed in BRU:
Although I can now see the "Date Taken" field, I cannot modify it. When I bring up the Options-Timestamps window, it is possible to modify "Date Created", "Date Modified", and "Date Accessed", but not "Date Taken". Am I missing something? Can this be added - Please?