I believe the actual MLB changed this rule a few years ago, and when they changed it, SCEA never updated the database to implement the change.
It always used to be (up until a few years ago) that the ONLY players eligible to be on the 40 man roster were those on the 25 man active roster, OR those on the MLB D.L. (I.L. now) on August 31st.
However, an injured player who fell into either of the two categories above, COULD be replaced by anyone on the 40 man roster on Aug 31st.
I believe MLB has since changed this to mean that anyone on the 40 man roster on August 31st is now eligible for the post season roster. But MLB The Show still does it according to the OLD playoff roster rules.