Well, at least, a functioning health care system shouldn't penalize for that sort of thing. We don't really have that in the US.
I don't know either, but the broader point is that people are referred to the ED by medical professionals for seemingly minor issues all the time, and that the incentives are all lined up to treat stupid shit in the ER rather than have someone tell them to go somewhere that makes more sense.
In that case part of the treatment they received was emergency evaluation for smoke inhalation. Just because they don't end up giving you drugs or doing surgery about it doesn't mean the assessment wasn't a valuable service.
Isn't it CYA for any EMS to recommend you visiting the hospital, so they just say it to anyone. That allows them to later say that you failed to follow recommended advice.
I feel fairly comfortable assuming that they were being seen for a minor-to-moderate burn.