If that's so, how would you explain the fact that big sites like Ask rank high for a ton of keywords with a really short article and little to no backlinks to the exact pages that are ranking high?
I get what you mean, though, but you are not entirely correct. While it is more important to have top quality backlinks to the exact page you are trying to rank for a specific keyword, it does help to naturally rank higher in the SERPs if you have a high pagerank root domain.
A page's SERP position is based only on the backlinks targeting a keyword.
No longer true. Please update your OP.