The links blue gave you are not in-store stock checkers.
that's obvious by ongoing discussion - so why do we keep referring to them?
The site also apparently uses/scrapes data from the online sites. Considering the fact that Target hasn't opened up on-line ordering for PS4 at all on their site, yet there's availability of the PS4 at stores means the tool is simply, at best a tool of available on-line stock at a given time.
Online stores are effectively separate entities than the local brick/mortar stores and the data on these sites are currently bound to data as the merchandise flows into (and is sold out of) the respective local stores. What is apparent is that Target (and other stores) are obviously not getting consistent stock/supply of the consoles from Sony in this regard (i.e. the distribution channel is supply constrained for a variety of unknown reasons) as compared to the X1...