Well, given his premises it’s still a coherent argument, so he isn’t begging the question or anything. It isn’t then quite right to say
Good thing I don’t have a problem with split infinitives then.
Well, given the premises of the analogy, that analogy is coherent as well. He is begging the question by implicitly assuming that split infinitives are ungrammatical, so naturally there has to be another reason ‘to boldly go’ is grammatical. Voila: it’s a completely new type of compound verb that uses adverbs. Never mind that the exact same rules for adverb-verb relationships work within the infinitive as without, and there’s no reason to say “He boldly went” has a compound verb in it. “To where boldly go” is ungrammatical because “where boldly <verb>” is not grammatical, not because that’s a “real” split infinitive; you couldn’t use it without the infinitive anyway except in archaic syntax.
Mind, I say this as someone whose major was in Linguistics and who happily bought the most insane crap in Syntax class that was necessary to explain why certain English constructs are grammatical. It’s just a convoluted explanation that’s neatly circumvented by simply allowing that infinitives may be split in English.