What does count as taking damage?

I was wondering about the rules behind the "no damage" achievements. I've found these on the older Binding of Isaac Wikia's page.

What counts as "taking damage?"

• Getting hit by an enemy, enemy projectile, bomb
• Purchasing an item from the Devil Room.
• Spike door in the Curse Room.

What doesn't count as "taking damage?"

• Using the Blood Donation Machine or IV bag.
• Damage taken from the Devil Beggar.
• The "Bad Trip" or the "Health Down" pill effects.
• The Razor Blade and Blood Rights items.
• Using a "Health up!" pill.
• Taking damage while under the effect of Holy Mantle

I know that Holy Mantle is a new item, so this seems to be an updated list, but it's on the old wikia, so the question is: is this list reliable for Rebirth too?
I need to know if Devil Deals still count as damage taken.

Losing or gaining health (upgrades / downgrades) isn't seen as damage, for example:

• Health up / down pill
• Devil deal
• Black market deal
• Guppy's paw (converts red hearts into soul hearts)

Stuff that deals damage:

• Bad trip pil
• Items that reduces / damages health (IV bag, blood rights)
• Blood banks
• Enemy contact / attacks / projectiles (not all enemies have contact damage)
• (bomb) explosions (unless when you have Pyromaniac)
• Spike door to the curse room
• Devil beggar

Items that help you in a run:

• Holy mantle (automatically blocks the first damage taken)
• Infamy (Can block projectiles on the side Isaac is facing)
• Lost Contact (Block enemy projectiles with your own projectiles)
• Gnawed Leaf (enemies cannot damage you when you're in statue form)

Source: experienced it myself: clearing parts of the game without receiving damage

Achievements:

Basement Boy

Beat basement without taking damage.

Spelunker Boy

Beat caves without taking damage.

Dark Boy

Beat depths without taking damage.

Mama's Boy

Beat womb without taking damage.

Dead Boy

Beat Chest or Dark Room without taking damage.

Synergies:

Lost Contact

• Piercing tears (tears are not destroyed on blocking enemy projectiles)
• Brimstone / Technology (laser will destroy all tears in it's path)
• The Ludovico Technique (floating tear cannot be destroyed, but will destroy projectiles)
• Mom's knife (Knife cannot be destroyed, but will destroy projectiles)

Gnawed Leaf

• Midas touch (when enemies hit you, they are turned into gold statues)
• E coli (when enemies hit you, they are turned into poop)
• The virus (when enemies hit you, they are poisoned)
• Gemini (Gemini will auto attack near enemies)
• Ball of bandages / cube of meat (damages enemies near / around you)
• Sacrificial Dagger (damages enemies near / around you)
• Daddy Longlegs (foot stomps enemies automatically)
• Leech (The leech will automatically attack and chase enemy around the room)
• Lil' Haunt (Lil' Haunt will automatically attack and chase enemy around the room)
• Demon Baby (Demon Baby will automatically attack enemies in range)

According to GameFaqs, it seems that in Rebirth Devil Deals no longer count as damage taken, unlike the original Binding of Isaac.