This is not hard to do. I can give you several instances where I've either done it myself or seen others do it, but I'll cite only two:
I have a 4th great-grandmother named Mary WEBSTER, who married my 4th great-grandfather John WINSLOW on 14 Apr 1796. I had Mary as being born in Kingston, New Hampshire on 11 Dec 1772 to Captain Jacob WEBSTER and Elizabeth GEORGE.
Then I ran into a problem: there was another Mary Webster who was born one week after, on 17 December, also in Kingston, to John WEBSTER and Mary CARTER.
This brought up the question, to which set of parents was my ancestor born? Every family tree on Ancestry.com that I found gave Jacob and Elizabeth as her parents... but of course family trees are often unreliable, and certainly can't be counted as valid sources.
I had to find evidence. The marriage record I found on FamilySearch didn't list the parents' names, and I had no death record.
A breakthrough finally came in the form of a death notice for her on GenealogyBank: it gave her father as Captain Jacob Webster, who had been a soldier in the War of American Independence, and even gave some details of his service. So now I knew that her parents-- and my ancestors-- were Jacob and Elizabeth.
Funnily, another example involves Mary's mother Elizabeth... I had erroneously had Elizabeth GEORGE as being the daughter of Micah GEORGE and Mary FAVOR. Then I realized that, while Micah and Mary did have a daughter Elizabeth, this Elizabeth George married a John JONES and died in Hopkinton, as did her parents. The parents of my 5th great-grandmother Elizabeth, who died in Kingston on 13 Mar 1824 and was buried there, are still unknown.
The moral of these two stories: different people with the same name, especially when born about the same time and in the same area, can easily be mixed up.
Jacob WEBSTER (1745-1836) m. Elizabeth GEORGE
Mary "Polly" WEBSTER (1772-1861) m. John WINSLOW
William WINSLOW (1800-1860) m. Mary "Polly" SEVERANCE
James W. WINSLOW (1838-1906) m. Elizabeth A. MACE
Bessie Maud WINSLOW (1886-1970) m. Frank Bailey PALMER
Dorothy Elizabeth PALMER (1918-1984) m. Henry Richard HOWES
S. HOWES (1937-1999) m. my father