I do not think that the fact checkers were checking whether the words of another were literally quoted nor is that important.  What is important are the conclusions and implications to policy and the nation.  If I say it will rain on Weds and somebody says that I said the streets will get wet Weds, they are asserting that my literal comment includes the consequence of wet streets.  It is so unimportant whether someone's exact words were quoted.  The implications for the country of those words are.