I have the answer you are looking for.
I worked on a website and targeted four keywords. The only thing I did was build high quality content. It took A WHOLE YEAR but it came from nowhere to number 2 for one of those keywords. Up to this day I still post content on that site. The keywords I would say have some medium high competition to them too.
If you are curious, I have spent two years doing this same thing on this site. No backlinks. Just content.
*EDIT*
These were not longtail keywords
IF you add content regular basis i thing it will help you to get PR but to get serp Ranking you must have to do some backlinks
0 backlinks cant get your site SERP Ranking (My opinion)
It can be done and i prefer to build such websites
this is my latest project - started 4 month ago, haven't build a single link, yet i do have ~240 now (naturally)
~700 posts. pretty happy about it and don't give a damn thing about the next google update
This statement is wrong for the PR part. PR is directly linked to PR flow from backlinks.
To answer OP questions, yes it is possible as far as your content is receiving some backlinks as your visitors are sharing it. Unless you are trying to rank for a similar kw as "fruhjtilapus" (where BHW will be your competitor soon), where in that case you cank rank solely on content.
yesterday i got 14K unique and 140eu
nearly all my kws in top10