Rules question – #dnd

I probably would have just asked this question via twitter but it’s a bit long for that.

I’m confused about dying in fourth edition.  Specifically, I am unsure of how the Heal skill works in relation to it. I’m going to quote a few rules and then my interpretation of them to see if you all agree.

Ok, first we have the definition of dying in 4e:

• You’re unconscious.
• You’re at 0 or negative hit points.
• You make a death saving throw every round.

Here are the rules on Healing the Dying:

When you are dying, any healing restores you to at least 1 hit point. If someone has stabilized you using the Heal skill but you receive no healing, you regain hit points after an extended rest.

HEALING A DYING CHARACTER

Regain Hit Points: When you are dying and receive healing, you go to 0 hit points and then regain hit points from the healing effect. If the healing effect requires you to spend a healing surge but you have none left, you are restored to 1 hit point.

Become Conscious: As soon as you have a current hit point total that’s higher than 0, you become conscious and are no longer dying. (You are still prone until you take an action to stand up.)

And here are the rules on the Heal Skill (specifically First Aid):

Make a Heal check to administer first aid.

First Aid: Standard action.
DC: Varies depending on the task you’re attempting.
Use Second Wind: Make a DC 10 Heal check to allow an adjacent character to use his or her second wind without the character having to take an action to do so. The character doesn’t gain the defense bonuses normally granted by second wind.
Stabilize the Dying: Make a DC 15 Heal check to stabilize an adjacent dying character. If you succeed, the character can stop making death saving throws until he or she takes damage. The character’s current hit point total doesn’t change as a result of being stabilized.
Grant a Saving Throw: Make a DC 15 Heal check. If you succeed, an adjacent ally can immediately make a saving throw, or the ally gets a +2 bonus to a saving throw at the end of his or her next turn.

Here is my question…

If  a character is dying but has not used his Second Wind in that encounter the character attempting First Aid can opt to go for the easier DC 10 Heal check.  This would restore the dying character to a number of hit points equal to their Healing Surge amount and burn one of their healing surges.  If they have no healing surges left it would restore them to 1 HP.  If the dying character has already used their Second Wind for the encounter all that can be done for them is a stabilization check.

Am I interpreting that correctly?