What information are you basing this on? I am unaware of any credible source that believes anything close to that. The sheer numbers of MLRS launchers needed to accomplish what you're talking about without even taking into account our MLRS' inability to penetrate the heavy rock a lot of those pieces are under makes your idea extremely unlikely.
This will probably never happen again, so mark your calenders, but I agree with eskimospy. I haven't been stationed in Korea, so I have no first hand knowledge, but the sheer numbers involved make it mathematically impossible for that scenario to be true. And as pointed out, most pieces are believed to be fortified in mountain redoubts, on tracks, mobile, etc., making them very difficult to accurately strike.
Plus, that doesn't even get into airspace deconfliction for 10,000+ separate projectiles... and the time it would take from the first report of incoming to get retaliation cleared through the White House... get the systems manned, activated, and fired, you are talking many minutes... bottom line it is simply impossible to avoid massive destruction of Seoul.