There are plenty of places they could have inserted a line or two to explain it, too. When Master Chief says his line about the Covenant being more fanatical on the first mission, Cortana could have come in and been like "I scanned their battlenet, and it looks like they're a splinter faction looking for something on this planet". Or there could have been something int he crash site on the second mission that said the same thing. The radio with the Elite repeating "Didact" was something, but not nearly enough.
Really anything to make it clear that these Covenant aren't The Covenant would have helped a lot. The closest they ever come is in the description of SpOps episode 4, which refers to "cult leader Jul 'Mdama". But this tiny bit of information is too little, too late, in the wrong place.
