Technically it means "naturally" which (to me, natural UK English) reads to me as slightly less sarcastic than "of course", especially if you get the "of COURSE" intonation (implies "the little shits" at the end of the sentence to me, if you see what I mean. "Naturally, the BBC has the news" - good job, fellas! "Of COURSE, the BBC has the news" - the little shits, running around wasting our money on this, probably stealing from rubbish bins.)
You’re not alone! I remember natch having a connotation of bragging, too, e.g. “I played my new set last night. Three women gave me their numbers. Natch.”
I may have put too much thought into this.