And of course you left out the weasel words thereafter:
Readers should bear in mind that, given the vagaries of human memory, remembered dialogue is rarely the same as actual recordings and transcripts. At the same time, it is no more nor less accurate than many other recollections.
Which means there are two types of quotes in this article:
1) Those which are public and on some kind of record and
2) Those which are recollection
The quote you gave does not speak to 2, it speaks to 1 as a way to make sure people do not get confused when reading the article and think that he spoke to certain sources. It's a way of covering the source's asses. As for 2, the same standard applies to journalistic quoting in general: for instance, it is unlikely you will be able to sue someone successfully for misquoting you (ie: libel) if the general meaning of the quote is the same.
Readers should bear in mind that, given the vagaries of human memory, remembered dialogue is rarely the same as actual recordings and transcripts. At the same time, it is no more nor less accurate than many other recollections.