They don't think you're a tourist, so you need a proper visa to stay longer. I know that in the past they didn't care and people lived literally for years just on visa waivers + border runs, but this isn't the case anymore.
they want only "real" tourists to come on visa waiver/tourism visa, while everybody else is also welcomed, but with an appropriate visa. The OP clearly isn't a tourist, as he mentioned wanting to get the DTV, so he's planning to stay in Korea for more than 3 months, maybe continously.
I know it's odd they don't disclose what data exactly was incorrect, but besides the name (including middle name, etc.) sometimes there are problems with the date of birth, etc.
Might be a stupid question, but did you applied twice, by any chance? Maybe one application was approved and the other rejected. Do they have the same application number?