Oh man. Sorry to hear that. Does the owner's manual actually say that you have to wipe the detergent off of the washer between uses? If it doesn't say that, I'd push back on them and make them cover this under warranty. I'm sure they don't WANT to cover it, but make them cover it anyway. Furthermore, read through your Sears warranty to be sure that it specifically excludes rust. If it doesn't specify that, you might have some legal ground to go after Sears to cover this, as well. There's just no excuse for a washer that is so new to rust at the top! Sounds to me like the powder coating process wasn't done right at the factory.
I have a front-loading Samsung VRT steam washer that's 6 years old now, and except for a few small issues after we moved (I suspect the movers dropped it, to be honest) it has been a workhorse. I do about 12 loads of laundry per week and that thing just trucks right along. (You know, if you can manage to get them to give some of your money back and/or if they let you get a new washer... ;)
ETA: You know what I would do about that e-mail from LG? I'd go onto their Facebook page and post not only your problem, but their response. Call them out publicly on it. Tell them that they have just advised to you to do something that will in all likelihood void your extended warranty with Sears (because you know Sears will use any excuse not to honor their extended warranty). I'd just keep on going with this, and not accept their suggestion that you repaint your own, almost-new washer. That's just absurd. Follow up with phone calls... just pretty much go from supervisor to supervisor until they acknowledge that there was a manufacturing defect that they need to fix for you. If THEY want to send a repair guy out there to sand down and re-paint that part of the washer, fine. This shouldn't be on you, though.