I am certain that EC is not chapped lips or just a wound. For example, our biopsy cut just healed in ten days and chapped lips should concern all the lips. Our EC is well-delimited, the area which isn't affected is totally healthy.
About the fact they tell that 'skin condition can heal spontaneously', well I don't really care.
My mom have some brownish marks on her face, maybe because of the sun and our origin, she visited a derm many years ago and we visited her again for my EC and she still told my mom that 'skin condition can go away spontaneously' you know, like if after years and years, cold turkey, nothing left!
It seems that this expression is just very common and simply means 'we don't know what you have but this can disappear one day, don't give up!', not much more. :)