A Google search will net you a number of YouTube video recorders, including this one, demoed right on the site:
I can't guarantee the video will be editable in Premiere Elements though and, if it is, how high the quality will be. You'll likely be dealing with some pretty strange codecs.
MPEG_Streamclip allows you to capture video from YouTube and any URL. It is also a tool recommended here and at Muvipix for converting files to DV-AVI which are fully compatible with Premiere Elements.
Hopefully the FAQs will be back up soon, these give details on how to use MPEG_Streamclip. For now here is the link to it: