after the change to "Enchantment - Aura", the wording is also a little clearer. Threads of Disloyalty now reads like this:
Enchant creature with converted mana cost 2 or less.
I guess Krinn said everything that really matters, but for the record:
702.5a Enchant is a static ability, written "Enchant [object or player]." The enchant ability restricts what an Aura spell can target and what an Aura can enchant.
Meaning that the creature needs to have the mana cost while targeting (which it has as a morph) and without pause (i.e. never when a player would get priority) while it's enchanted.
707.5 At any time, you may look at a face-down spell you control on the stack or a face-down permanent you control (even if it's phased out). You can't look at face-down cards in any other zone or face-down spells or permanents controlled by another player.
When you got control of the morphed card, you can look at it and then decide whether or not to pay its morph cost.
To Avish:
110.6 A permanent's status is its physical state. There are four status categories, each of which has two possible values: tapped/untapped, flipped/unflipped, face up/face down, and phased in/phased out. Each permanent always has one of these values for each of these categories.
Meaning that being phase down is a state, and changing that state doesn't make it automatically a new permanent.