Does he mean the rule to determine the next blockchain requires knowing the state of currently bonded validators?
This “out-of-band authentication only necessarily once” property is what Vitalik calls weak subjectivity. In this context information is said to be “objective” if it can be verified in a protocol-defined manner, while it is “subjective” if it must be authenticated via extra-protocol means. In weakly subjective consensus protocols, the fork-choice rule is stateful, and clients must initialize (and possibly sometimes renew) the information that their fork-choice rule uses to authenticate the consensus. In our case, this entails identifying the currently bonded validators (or, more probably a cryptographic hash of the validator list).