In the specific case of OSPF, the peer OSPF and BGP router-ids must match. Both router-ids are including in the routing information the peer sends.
In the description of the synchronization feature, the “…does not use that information…” refers to installing the BGP route in the default routing table and advertising it or not to the neighboring peers.
This statement is not consistent especially in the case of OSPF and static routing with higher than BGP administrative distances: the routes are not deleted from the routing table evenif they’re marked as “not synchronized” in Loc-RIB…
In EIGRP the statement is effective but not efficient due to the process loop it creates by adding and deleting the corresponding routes infinitely…
