That’s not really how the story goes, but you’d never know it from reading the horribly truncated modern versions. To quote Irving’s original (which is up on Project Gutenberg, among other places):
It is true, an old farmer, who had been down to New York on a visit several years after, and from whom this account of the ghostly adventure was received, brought home the intelligence that Ichabod Crane was still alive; that he had left the neighborhood partly through fear of the goblin and Hans Van Ripper, and partly in mortification at having been suddenly dismissed by the heiress; that he had changed his quarters to a distant part of the country; had kept school and studied law at the same time; had been admitted to the bar; turned politician; electioneered; written for the newspapers; and finally had been made a justice of the Ten Pound Court. Brom Bones, too, who, shortly after his rival’s disappearance conducted the blooming Katrina in triumph to the altar, was observed to look exceedingly knowing whenever the story of Ichabod was related, and always burst into a hearty laugh at the mention of the pumpkin; which led some to suspect that he knew more about the matter than he chose to tell.
So Ichabod is alive and doing fine, and Brom (who often gets accused of murder) is a rather rough practical joker, but no killer. The final paragraph of the story proper establishes that the local gossips refuse to believe the farmer’s testimony and instead form a new piece of folklore around Ichabod being carried off.
All of which ties into the overall theme of believing too much in fantasy leading to bad results. Ichabod not only believes implicitly in the Horseman superstition, he also dreams of marrying a wealthy young heiress in defiance of all reason. He only gets a good ending when he leaves Sleepy Hollow (and his fantasies) behind for good. Brom never buys into any of this guff and has more realistic expectations about getting hitched, and he’s very definitely the winner of the story.
There’s also a postscript conversation between the storyteller and a listener who has his doubts about the tale’s veracity and the storyteller subtly mocking him for taking everything too seriously, then admitting he doesn’t believe half of it himself. It’s pretty funny in a wry way, and hardly ever gets printed any more.
Whether Grimm would be bound by the original or mutilated version of the story is up for debate, but just the fact that the “carried off ending” is merely an edited variant probably gives him an easy out - assuming he doesn’t mind playing at being a schoolteacher, lawyer, politician, newswriter and judge for however long it takes to wriggle free. Wouldn’t make Grimm like Rambler any better though. 