I finished watching a PBS American Experience episode on former US President Ronald Reagan and coincidently stumbled on an article by John Grenham in the Irish Times of 31 January. He uses Reagan as an example of the hazards of drawing conclusions about connections too readily.
Take the Irish ancestry of Ronald Reagan. The earliest documented ancestor is Michael Regan, who married in England in 1852 and recorded his father as Thomas. The English 1851 census (very fortunately) gave Tipperary as his place of origin and his age as 21. So far, so good. The researchers who searched Tipperary parish registers did indeed find a Michael, son of Thomas Regan, baptised in Ballyporeen in 1830. But at least 20 of the 53 Catholic parishes of Tipperary have no records for the years around 1830. Both Michael and Thomas are unimaginably common forenames and there were at least 60 Regan households in the county at the time. So it is perfectly likely that more than one Michael, son of Thomas, was baptised in the relevant period.