Everio video is a strange beast, and they regularly give people problems. It's doubtful that installing any codecs will make them perform more efficiently, since JVC apparently created them with the intent of making them non-standard.
The FAQs to the right of this forum offer all we have on them.
I looked at the link to the Elements Organizer Help which you referenced it would seem to imply that MOD is supported for the Organizer (because it is listed in the first chart that vob is supported and then is not listed in the second chart for files which the Organizer does not support).
However, MOD is listed as a type that Premiere Elements does not recognize. So as Steve references, you may need to convert your MOD files anyway.
Yet if you are currently importing the MOD files to the Organizer and you are able to play them back from within the Organizer but see the film strip icon in the Organizer thumbnail, then it might be possible for you to find and install a codec capable of extracting the first frame from a MOD file. However I can give you no clues to what such a codec is.
Will Adobe fix this problem of no image in the Organizer thumbnail for MOD files - I would not be optimistic.
Therefore, if you will be converting the MOD files anyway for use in Premiere Elements, it might be the more practical alternative to make thumbnails from the converted video files. Note that you might need to use the Organizer change date/time command to have the thumbnails for the converted video files appear in the correct sequence within the Organizer.
Please share that MOD files. I will check the files or share the MHZ of the file which you are trying to import in PSE . It is easily understand right click in properties in premiere elements project window.