The confusion stems from the fact in Ancestry.com, there is a database record that has
Name: Ann Putname
Gender: Female
Birth Year: 1629
Spouse Name: Henry Kinne
Spouse Birth Place: En
Spouse Birth Year: 1623
Marriage Year: 1650
Number Pages: 1
Yates Publishing. U.S. and International Marriage Records, 1560-1900
That and the Kinney/Kinne family were close to the Putnam family in Salem. Henry Kinne, Sr supported the accusations of Ann Putnam against some women... and later some Kinne children were put in the guardianship of the Putnams... so that makes many people theorize that Henry's wife Ann must have been a Putnam and maybe an aunt or older cousin of Ann Putnam the accuser.
Secondly, in Torrey's New England Marriages, he has an entry
>>>KINNE, Henry 1 (1624- ) & Ann HOWARD (1632?-1680+); b 1651(2?), 3 May 1650; Salem?<<<
However, he did not have any vital record support nor has anyone else been able to substantiate that this is correct.
Thirdly, some genealogy sources say that Henry had 2 wives named Anne.... It is unclear if that was true or if it was just a way to resolve two theories that suppose his wife was Ann Putnam or Ann Howard based on #1 and #2 above, or maybe a composite Ann Putnam Howard who married Henry Kinne in 1650.
Many people involved with more recent Kinne family research seem to think that Ann was someone else entirely and it was all a mix up.
So it gets passed along like the telephone game and gets written as if a fact.