'John Whiteman ... was born August 18, 1772. ... John Whiteman ... died May 8, 1827. ... Rebecca de Remer [first wife of John's son Daniel Jackson Whiteman] ... died May 8, 1827.'
While it is possible that John and his daughter-in-law died the same day (accident or disease), it is also possible that the author confused the dates, and recorded John's death incorrectly. If he died in 1827, it is not clear who the John Whiteman in the 1840 census would be, unless it was a nephew aged 20-29 who was the head of the household with 3 people older than himself in the household. Other family trees do not provide a likely candidate for this.