It appears that there were two parts to the protection
From various sources throughout the books it becomes apparent that there were two separate aspects to the protection Harry had. The first was a more specific protection. This had nothing to do with Dumbledore, and was solely the result of Lilly's love. This specific protection prevented Voldemort's original curse from killing Harry, and it also prevented Quirrel from touching Harry. This aspect of the protection is dealt with in several places:
In the end of Philosopher's Stone Dumbledore partly explains the protection from Lilly's sacrifice:
“Your mother died to save you. If there is one thing Voldemort cannot
understand, it is love. He didn’t realize that love as powerful as
your mother’s for you leaves its own mark. Not a scar, no visible
sign ... to have been loved so deeply, even though the person who
loved us is gone, will give us some protection forever. It is in your
very skin. Quirrell, full of hatred, greed, and ambition, sharing his
soul with Voldemort, could not touch you for this reason. It was
agony to touch a person marked by something so good.”
In the end of Chamber of Secrets Tom Riddle says the following:
“So. Your mother died to save you. Yes, that’s a powerful
counter-charm. I can see now ... there is nothing special about you,
after all.
In the graveyard in Goblet of Fire Voldemort says:
“His mother left upon him the traces of her sacrifice.
. . . This is old magic, I should have remembered it, I was foolish
to overlook it . . . but no matter. I can touch him now.”
Harry felt the cold tip of the long white finger touch him, and
thought his head would burst with the pain.
We see from the above quotes that the protection from Lilly's love was limited to two things: It blocked the original Killing Curse, and it prevented someone who "has no love" from physically touching Harry. And in fact once Voldemort came back and took some of Harry's blood, he apparently overcame this part of the protection. As Dumbledore himself noted on that occasion:
“Very well,” he said, sitting down again. “Voldemort has overcome
that particular barrier. Harry, continue, please.”
The second aspect of the protection is more general. This part essentially made Harry's home a "safe zone". This protection was derived from Lilly's love, but was ultimately implemented by Dumbledore. What Dumbledore did was essentially apply Lily's love protection to the Dursley's home by channeling it through Harry's blood relation to Aunt Petunia.
At the end of Order of the Phoenix Dumbledore explains how this worked:
“While you can still call home the place where your mother’s blood
dwells, there you cannot be touched or harmed by Voldemort. He shed
her blood, but it lives on in you and her sister. Her blood became
your refuge. You need return there only once a year, but as long as
you can still call it home, there he cannot hurt you. Your aunt knows
this. I explained what I had done in the letter I left, with you, on
her doorstep. She knows that allowing you houseroom may well have
kept you alive for the past fifteen years.”
As you note in the question, this is what Dumbledore said was his own implementation:
“She may have taken you grudgingly, furiously, unwillingly,
bitterly, yet still she took you, and in doing so, she sealed the
charm I placed upon you.
Your mother’s sacrifice made the bond of blood the strongest shield I
could give you.”
In the beginning of Half-Blood Prince Dumbledore explains this aspect of the protection to the Dursleys:
“The magic I evoked fifteen years ago means that Harry has powerful
protection while he can still call this house ‘home.’ However
miserable he has been here, however unwelcome, however badly treated,
you have at least, grudgingly, allowed him houseroom. This magic
will cease to operate the moment that Harry turns seventeen; in other
words, at the moment he becomes a man. I ask only this: that you
allow Harry to return, once more, to this house, before his
seventeenth birthday, which will ensure that the protection continues
until that time.”
Thus, it seems clear from all the above quotes that Dumbledore implemented a magical protection in addition to the protection Harry already had from his mother's sacrifice. Dumbledore's protection was based on the original protection, and indeed could probably be termed an extension of the original protection.
It is interesting to note, though, that it is possible that other characters did not fully understand this distinction. In the beginning of Deathly Hallows there are several references to the protection of the Dursley home:
Moody dropped his sacks at his feet and turned to Harry. “As Dedalus
probably told you, we had to abandon Plan A. Pius Thicknesse has gone
over, which gives us a big problem. He’s made it an imprisonable
offense to connect this house to the Floo Network, place a Portkey
here, or Apparate in or out. All done in the name of your protection,
to prevent You-Know-Who getting in at you. Absolutely pointless,
seeing as your mother’s charm does that already. What he’s really
done is to stop you getting out of here safely.
“Now, your mother’s charm will only break under two conditions: when
you come of age, or” — Moody gestured around the pristine kitchen —
“you no longer call this place home. You and your aunt and uncle are
going your separate ways tonight, in the full understanding that
you’re never going to live together again, correct?”
In these two quotes, Moody apparently conflates Lilly's protection with Dumbledore's protection. It is possible that Moody was not fully aware of the mechanism of the protection, it is possible that he was simply being imprecise in his speech, or it is possible that a minor authorial error crept in here.
