I wouldn't even say the immune system, your body has a ton of nonspecific RNA-digesting enzymes floating around to patrol for exactly this sort of thing happening, even by accident, as cells can sometimes rupture. It's a problem enough that good RNA researchers have a reputation of being clean freaks. Some RNA labs I've been in had a lingering, slightly sweet smell, that's the nonspecific RNAase inhibitor that gets sprayed on everything.