"Material" in this case means "having something to do with LE's investigation."
There's no question, of course, that telling LE where and with whom you left your baby and when you last heard from her has something to do with a missing baby investigation. So this was a very technical question--did the judge need to TELL the jury that they had to make that finding? It was an attempt to get off on the technicality that the judge had not mentioned anything about materiality to the jury.
IMO the statute probably does imply a materiality requirement--e.g., you should not be convicted for giving false information to LE just because you (for whatever crazy reason) lied about what you ate for breakfast the morning your child went missing, which didn't cause LE to go off on a "wild goose chase," but you should be convicted for giving false information to LE if you give them a bunch of fake names and identifying info of suspects and witnesses. The court didn't even discuss this argument, though, perhaps because Cheney Mason's briefs (his associate's briefs, really) kind of sucked on that issue.
But I've learned my lesson a couple of times on this case, and I'm not gonna help them out by saying what should have been in the briefs. 
