The question says that Hindley’s claim to have “crammed Kenneth, head-downmost, in the Blackhorse marsh” is untrue. But is that right? Hindley only claims to have dunked the doctor, not drowned him. And some rough-and-tumble would be consistent with Kenneth’s later description of Hindley as having done him “many a rascally turn”:
“Hindley Earnshaw! Your old friend Hindley,” he [Kenneth] replied, “and my wicked gossip: though he’s been too wild for me this long while. There! I said we should draw water. But cheer up! He died true to his character: drunk as a lord. Poor lad! I’m sorry, too. One can’t help missing an old companion: though he had the worst tricks with him that ever man imagined, and has done me many a rascally turn. He’s barely twenty-seven, it seems; that’s your own age: who would have thought you were born in one year?”
Emily Brontë (1847). Wuthering Heights, chapter 17. Project Gutenberg.
Under this interpretation, Hindley’s assault on the doctor is evidence of his increasingly violent and impulsive behaviour following the death of his wife Frances. He was never particularly pleasant, but we are told that in his grief he abandoned all self-restraint:
As the girl† had anticipated, the child Hareton fell wholly into my hands. Mr. [Hindley] Earnshaw, provided he saw him healthy and never heard him cry, was contented, as far as regarded him. For himself, he grew desperate: his sorrow was of that kind that will not lament. He neither wept nor prayed; he cursed and defied: execrated God and man, and gave himself up to reckless dissipation. The servants could not bear his tyrannical and evil conduct long: Joseph and I were the only two that would stay.
Brontë, chapter 8.
† This is “the girl that usually brought our breakfasts” who ran to announce the birth and said, “You’re to nurse it, Nelly”.
So Hindley’s throwing the doctor into the marsh, his threatening Nelly with the carving-knife, and his dangling of Hareton over the bannister, are all evidence of this violent and unconstrained grief.
However, since we only have Hindley’s words, an equally plausible interpretation is that his claim to have soaked the doctor is an empty boast. This would be in keeping with his other threats, none of which he carries out: “I want to kill some of you: I shall have no rest till I do!”—”he [Hareton] deserves flaying alive”—“I’ll break the brat’s [Hareton’s] neck”—”unless, perhaps, I set the house on fire”. Peter Miles suggested that Hindley’s claim was a fantasy of revenge on the doctor for his predicting the death of Frances:
He [Hindley] does not mention Frances, but his boast that he has “just crammed Kenneth, head-downmost, in the Blackhorse marsh” is an angry fantasy of punishment deflected onto the doctor who had so bluntly predicted her death.
Peter Miles (1990). Wuthering Heights, p. 75. Macmillan.
This was the doctor’s absurdly insensitive speech to Hindley after the birth of Hareton:
“Earnshaw, it’s a blessing your wife has been spared to leave you this son. When she came, I felt convinced we shouldn’t keep her long; and now, I must tell you, the winter will probably finish her. Don’t take on, and fret about it too much: it can’t be helped. And besides, you should have known better than to choose such a rush of a lass!”
Brontë, chapter 8.
But, of course, Hindley’s resentment over this speech explains a real dunking in the marsh just as well as it does an imaginary one.