Why are SBAS-equipped planes exempt from the preflight prediction check?
The slide refers to ADS-B integrity, which requires a different integrity level than RNP. The ADS-B preflight check they refer to is a different than the check for RNP.
The FAA requires an integrity bound of 0.2 NM or less for ADS-B. For RNP2 (en-route) and integrity bound of 4 NM is sufficient. RNP-approach requires and integrity bound of 0.6 NM.
The probability of not achieving the integrity level required for ADS-B is significant for TSO C129 (SA ON) installations, much lower for TSO C196 (SA Aware) installations and insignificant for TSO C145/146 (SBAS) installations.
The better performance of thw SBAS installations is because SBAS does a few things to improve integrity:

it is an extra GPS satellite at a fixed (geostationary) position.
it supplies parameters for an error correction model that improve the accuracy of GPS signals received by the GPS receiver
it does its own integrity monitoring of the whole GPS system and reports any issues with GPS within 6 seconds to the WAAS receivers.