I would not recommend using third-party software (like PlayMemories) to import the video from the camera to your computer. This software may change elements of your video and cause issues like you're experiencing.
Premiere Elements includes Add Media tools for interfacing with cameras and camcorders. I highly recommend you use it to import any video or photos from your camera or camcorder to your computer and video project.
Further to Steve's comment I import photos and videos direct to PRE from my DSC-HX9V.
PlayMemories does have one very good feature though - if you want to trim your video, it can do so using smart rendering, meaning that it does not have to re-render the video when creating trimemd output.
Insanity is hereditary, you get it from your children.
Thanks for your help. It does import the videos with the correct dates and times, BUT is there a way to automatically have them placed in the folders with their respective dates (as PlayMemories does) or do I have to move them manually (using PE)?
The Elements Organizer should be able to arrange your files by date, event, people in them, location they were shot, etc. Though only dates (under the Events tab) is automatic.
Thanks. Problem resolved.