Story highlights Fiorina said Tuesday night that several respected generals were "retired early because they told President Obama things that he didn't want to hear"

But one of those generals, John Keane, retired years before Obama took office

Henderson, Nevada (CNN) Carly Fiorina on Wednesday didn't back down from her claim that certain generals retired from the Obama administration because of clashes with the president, even though one of those generals didn't serve in the Obama administration.

The Republican presidential candidate said in the CNN debate Tuesday night that Generals David Petraeus, Stanley McChrystal, James Mattis, John Keane, and Michael Flynn were "retired early because they told President Obama things that he didn't want to hear."

Fiorina was answering a question about how she would defeat ISIS, and one of her ideas was to "bring back the warrior class," as she called them.

While Mattis and Flynn appear to have left over policy differences, PolitiFact notes that Keane resigned in 2003, long before President Barack Obama took office in 2009. Petraeus, meanwhile, was forced to resign amid scandal involving an extramarital affair. McChrystal was forced out in 2010 after unflattering remarks about Obama administration officials were attributed to him and his aides in a Rolling Stone article.

Talking with reporters Wednesday after a town hall here, Fiorina was asked if she misspoke about Keane given the timing of his retirement.

Read More