EDIT: Realized I read everything except what was after the sentence in question...oops...I'll just leave this as a placeholder then...
EDIT 2: Nevermind...I thought I figured out what it meant, but when I read the rest I found myself decidedly unsure.
EDIT 3: Okay, I've never seen the quotation particle used with 話す, but that may indeed be what it is (since my particle book lists と話す in its examples of と), and so it may mean simply that he spoke about what they said.
EDIT 4: I'm really being spastic huh? Anyway, before I made edit 3, I considered that と may be acting as "against", as in "he spoke against what the NYT said." The reason I'm not completely satisfied with that is that my book says that usage happens after nouns... and I take that to mean that non-nominalized clauses are excluded.
EDIT 5: ...I hate myself right now... Okay, I think it may be saying that he spoke <EDIT 3 or EDIT 4> HOW the NYT said it. Which is fitting considering he talks about misunderstandings.