A lot of these things do say not to use an extension cord, even though plugging them into an extension cord is usually the only way they're going to be plugged in. I think they have to say that as part of the normal warning system. (It's kinda like how majority of toys say 3+, despite the fact...
Does it have a warranty with it? Some things have warranties where they might replace this if it was a malfunction on their part. Where the burn was, unless it wasn't hooked in properly, I'd say it’s just a malfunction. Did the breaker blow? Sometimes on things like this, the breaker will blow...