Why doesn't FIOS on Demand have CBS Person of Interest?
Because CBS is not making it available.
Verizon doesn't record these shows (unlike at least one other provider), it puts up the on-demand recordings provided to them by the various content providers.
Actually, it is not CBS, they don't own Person of Interest. Bad Robot Productions and Warner Brothers, the producers of Person of Interest, have retained the OnDemand/Streaming rights. CBS is only allowed to broadcast it over live TV.