Backlinks have some effect on the youtube video showing up in the SE for video requests in natural search, sure. However, I don't think it holds any major pull in youtube itself unless you get actual views, comments and most importantly - favorite votes, which is what you are seeing in the " 50-100 other youtube users listing..." comment.
Youtube is all about the fame of the video, views and favorite tags to it as far as making rank within youtube itself. It is user-generated, user-voted and user supported content that gets the best exposure and therefore, the higher ranking withn the service.
If you are simply trying to be found, backlinks and such play into it. However, being on the first page of google's natural video search results doesn't mean you are going to be the first in youtube or vice versa.
Hope that helps answer your question.