I have been experiencing the same issues and Verizon has never heard of it either.
If you long press to the right of the play button icon you will receive that pop up with Message options and from there you can save to SD card. However, transferring it to your computer is a little tricky. I just got an macbook pro and when I plug in the USB cord to my computer, all the true pix texts pop up and are easy to import over. I had to go to my finder and drill through the connected device folders on my phone and drag and drop the "video" pix onto my computer. It works and appears as a normal photo once onto my computer.