There is no single sub-set of "value" investing.  Take "Warren" as an example....he began his career by purchasing what he felt were very, very inexpensive businesses, albeit, often ones that had plenty of warts.  He evolved, over time, to buying good to very good businesses at a "fair" price.

There are still plenty of value investors that try and pay $0.50 for a $1.00 worth of assets (say, anyone buying HBC  or Sears for its real estate....is betting that HBC or Sears is worth more dead than alive).  

But a lot of value investors are willing to pay up (within reason) for a good business, with Buffett like "moats" around their business model.