A GoFundMe page, local media reports and her niece had said a man had throttled the 44-year-old before throwing flammable liquid on her and torching the wooden house.
But police on the Caribbean island said "very high quality" CCTV from a neighbouring house has "clearly demonstrated that no-one entered those premises for hours prior to the fire taking place".
Tyrone Griffith, Commissioner of the Royal Barbados Police Force, added investigators had found no smell of any accelerant and the fire was concentrated in the kitchen, where food was being prepared.
He told a press conference on Thursday evening: "At this stage there is nothing to indicate that there was an intruder at those premises.
"About 13.43 hours, suddenly the house went up in flames with the seat of the fire being concentrated in the kitchen area.
"The fire rapidly engulfed the house and residents and workmen on a nearby house quickly sprang into action to assist.
"They broke away a sheet of galvanise from the yard to gain entry and assisted in getting to the deceased who was found in the yard badly burnt."
He added that gas canisters were found in the kitchen and "the side of the saucepan was completely burnt away".
He said the "corrugated fence was fully intact apart from the sheet that was removed to provide access for the victim".
Mother-of-three Ms Crichlow, who had survived cancer twice and had two strokes in the past decade, was on the trip to help look after her disabled brother.
A post mortem examination found Ms Crichlow, of Colingdale, north London, died as a result of infection from the burns on August 6, Mr Griffith added.
One of her sons is Hartlepool United defender Romoney Crichlow-Noble, 20, and her other children are aged 10 and 26 years old.
They want to get her back home to Britain for burial and a GoFundMe page has raised nearly £20,000.
Her niece Ashley Best previously told PA: "The intruder broke in the house, then strangled her and then set her alight.
"I do not understand why it happened and we are all in a state of shock."
Mr Griffith added: "This matter is being treated as an unnatural death and intense investigations are ongoing."