Was the NYT article edited after the fact? That happens fairly often. I remember having to calm my gf down after she was so upset by the news that someone had their head bashed in with a fire extinguisher. It was definitely reported, and definitely false.
Here's the quote I see from articles alleging the NY Times reported and spread a false story: "Mr. Sicknick, 42, an officer for the Capitol Police, died on Thursday from brain injuries he sustained after Trump loyalists who overtook the complex struck him in the head with a fire extinguisher, according to two law enforcement officials."
As best as I can tell the fire extinguisher was a different event in which officers were struck by a thrown extinguisher. Sicknick did suffer brain injuries (a stroke). The medical examiner hasn't attributed fault to possible exposure to bear spray that some protestors might have used, so his stroke is determined to be from natural causes. I think we have to wait for the accused protestor's trials to determine finally whether they assaulted Sicknick.