While you need ID, all that proves is that you have been asked to attend. You can get access to the building (ok after hours) by signing up to a meetup and providing your name. Also by virtue of the work they do, relative strangers will come in frequently as sources, experts, etc.

Shootings tend to happen relatively quickly (though often longer than people think the Virginia Beach shooter wasn't contained for 15 minutes), but they tend to have very long and potentially dangerous sweeps to clear the area. You don't want a response team to accidentally shoot a guy holding a stapler or something.

The NY Times building is a single block from Times Square where there are enough heavily armed response teams to depose several island governments 24/7. Also being in the area somewhat regularly there are regular and counterterrorism police directly in front and across the street often during daylight hours.

The Times is kind of the exception that proves the rule. If you aren't literally feet from an armed response that can bring down everything from an armored car to a helicopter (only rumored, but repeatedly so) it probably won't do as much good. In their particular situation though, I suspect it could save lives if a rare event occurs. Which is always a hard thing to balance.