Hagrid Flies? Really?

I've often wondered about this and it has struck me again as I read J.K.'s first book in French. When Harry asks Hagrid how he got to the rock in the middle of the sea to deliver Harry's Poudlard (Hogwarts) letter to him, Hagrid tells Harry he flew there.

J.K. never explains how Hagrid flew there.

He could not have come on a broom for two reasons: first, he doesn't bring a broom back to London and, second, it is explained in a later novel that Hagrid is too heavy for a broom.

He could not have come via Sirius' motorbike (upon which Hagrid had flown the infant Harry to Privet Drive in the first place) since he would have had to leave it on the rock when he takes Harry away with him on the boat.

He could not have apparated there, since Hagrid is never shown to have mastered Apparition, he was kicked out of Hogwarts in his third year before he could have taken lessons and earned his Apparition license, and, besides, Apparition requires a fully functioning wand. Hagrid's was broken in half when he was forced to leave school.

Since it is established in The Deathly Hallows that only Voldemort can fly on his own (several members of the Order tell the others with amazement that "Voldemort can fly" after the Death Eaters ambush the seven Harrys), it would seem to me that there are only three possible explanations as to Hagrid's claim that he had flown to the rock in the sea:

1) He flew in on a Hippogriff or Thestral, which delivered Hagrid and then flew away again. I wonder if either a Hippogriff or a Thestral would be strong enough to carry Hagrid, however;

2) He was taken there by someone else via Side-Along Apparition, though I don't understand why that person wouldn't have stayed to talk to Harry; or

3) Hagrid is not being truthful about how he got to the rock.

It's one of the few details in the entire Harry Potter series that doesn't make sense to me, that doesn't seem to follow Rowling's usually consistent rules for the wizarding world.

I know. I'm probably holding J.K. to too high a standard: this is the first book and it's likely she hadn't quite worked out all of the details of her magical world at this point.

More on flying tomorrow.