I'm not sure, but I think you're confusing split infinitives with split verbs. Split infinitives are definitely a schoolmarm invention (borrowed from Latin, where the infinitive is an inflection and thus inseparable). I think split verbs are here referring to the possibility of separating verbal auxiliaries from their verb.
I think by "split verb" he's referring to "separable verbs", where a particle, resembling a preposition, moves to the end of the sentence. This sometimes occurs in English, apparently violating the "schoolmarm" rule to not end sentences with a preposition.
