I personally wouldn't say mages burn decks require no skill, they require a decent bit to know when you have to freeze and when you can take damage and shit(unless you have an obscene hand but that's similar for most decks really). What it is however is extremely unfun to play against. In MTG I never felt the burn decks were that bad, back when I played at least, cause there were so many shit that would ruin the deck. Destroy lands? Have fun never casting your fireballs for more than 3-4damage. Discard? Oh you needed that spell to do damage? Suck it. Also it was harder to keep both the control aspect and the burn aspect in harmony, because of the color system and shit. In Hearthstone, it's very simple to play both blizzards/cone of colds/ice blocks/frost armors/sheep/whatever along with fireball/pyroblast/giants/whatever, since all the mana is the same.
It's also strong because there aren't many different things you can do in the game, there is a kinda mill deck but it works so so in this game since you can't prevent people from playing stuff as much/can't remove their mana, mostly the game is you either equip weapon and kill shit, drop mobs then kill shit, use spells to do direct damage to kill shit, use spells that are pure removal(few of these overall and fairly class specific) or use chargers(mobs that act like spells, other than they can't bypass taunt which sucks a lot quite often). Most of it is countered by mage decks.
That said I've read a few posts on reddit from people playing slow heal decks doing well against mages. They lose badly against aggro locks or aggro rogues, but since mages are so dominant currently, if you win most of your mage games you're still gonna be way positive. That's one thing I feel is different from MTG, there's a lot less potential spells in your deck(max 2 per deck vs iirc max 4 for MTG) and you have more health too. So it makes it hard to sustain the assault as a mage unless giant play, but most slow decks can deal with giants, either with big game hunter, superior big mobs, direct removal or direct nukes(starfire+wrath or avenging wrath+hammer of wrath kill giants/rag/anything with 8 for example).
