Kheru Spellsnatcher
Oracle Text
Morph
(You may cast this card face down as a 2/2 creature for . Turn it face up any time for its morph cost.)When Kheru Spellsnatcher is turned face up, counter target spell. If that spell is countered this way, exile it instead of putting it into its owner's graveyard. You may cast that card without paying its mana cost for as long as it remains exiled.
Card Rulings
9/20/2014 You can target a spell you control with Kheru Spellsnatcher’s triggered ability. This will give you the ability to cast the card later without paying its mana cost.
9/20/2014 Because you’re already casting the card using an alternative cost (by casting it without paying its mana cost), you can’t pay any other alternative costs for the card, including casting it face down using the morph ability. You can pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.
9/20/2014 If the card has in its mana cost, you must choose 0 as the value for X when casting it.
9/20/2014 Morph lets you cast a card face down by paying , and lets you turn the face-down permanent face up any time you have priority by paying its morph cost.
9/20/2014 The face-down spell has no mana cost and has a converted mana cost of 0. When you cast a face-down spell, put it on the stack face down so no other player knows what it is, and pay . This is an alternative cost.
9/20/2014 When the spell resolves, it enters the battlefield as a 2/2 creature with no name, mana cost, creature types, or abilities. It’s colorless and has a converted mana cost of 0. Other effects that apply to the creature can still grant it any of these characteristics.
9/20/2014 Any time you have priority, you may turn the face-down creature face up by revealing what its morph cost is and paying that cost. This is a special action. It doesn’t use the stack and can’t be responded to. Only a face-down permanent can be turned face up this way; a face-down spell cannot.
9/20/2014 Because the permanent is on the battlefield both before and after it’s turned face up, turning a permanent face up doesn’t cause any enters-the-battlefield abilities to trigger.
9/20/2014 A permanent that turns face up or face down changes characteristics but is otherwise the same permanent. Spells and abilities that were targeting that permanent, as well as Auras and Equipment that were attached to the permanent, aren’t affected.
9/20/2014 At any time, you can look at a face-down spell or permanent you control. You can’t look at face-down spells or permanents you don’t control unless an effect instructs you to do so.
9/20/2014 You must ensure that your face-down spells and permanents can easily be differentiated from each other. You’re not allowed to mix up the cards that represent them on the battlefield in order to confuse other players. The order they entered the battlefield should remain clear. Common methods for doing this include using markers or dice, or simply placing them in order on the battlefield.
9/20/2014 If a face-down permanent leaves the battlefield, you must reveal it. You must also reveal all face-down spells and permanents you control if you leave the game or if the game ends.
702.60b
... Triggered abilities trigger and are put on the stack as normal while a spell with split second is on the stack.
EDIT: According to the comprehensive MtG rules...
702.36d
Any time you have priority, you may turn a face-down permanent you control face up. This is a special action; it doesn’t use the stack....
707.11.
If a face-down permanent would have an “As [this permanent] is turned face up...” ability after it’s turned face up, that ability is applied while that permanent is being turned face up, not afterward.
That makes it sound like the ability would occur without being put on the stack, but it is my understanding that since it's a triggered ability, the trigger is what is applied when the permanent is being turned face up, not the actual ability.
603.2.
Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. The ability doesn’t do anything at this point.
603.3.
Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority. See rule 116, “Timing and Priority.” The ability becomes the topmost object on the stack. It has the text of the ability that created it, and no other characteristics. It remains on the stack until it’s countered, it resolves, a rule causes it to be removed from the stack, or an effect moves it elsewhere.
So, in the end, I guess I really don't know. If seems to depend on whether the triggered ability is considered to be triggered or if it just applies.