There's a couple things to unpack here but I'll start with the idea of bringing the meat to room temperature before cooking.
This is a myth. Despite the ostensible respectability of those sources (though honestly I find NY Times cooking to be extraordinarily overrated) I defy you to find anyone who has done a side by side comparison and found the room temperature version to be superior. There are however no shortage of sources debunking this myth, e.g.:
https://www.seriouseats.com/old-wives-tales-about-cooking-steak
https://www.youtube.com/watch?v=GZx2n_sOGj8
The theory is that this will cook the meat more evenly, and this is perhaps true if your goal is in fact to have something that is gray from center to exterior, but that is NOT usually the goal. Rather the goal is usually to have a nice brown crust and a medium rare interior. If the meat is cold when it goes in the oven, that means the center will take longer to come to doneness - giving your exterior more time to dry out and develop a nice crust when you do your final sear. And before you ask, "won't that lead to the dreaded gray band?", no, it won't, at least not at a slow cook temp, because the heat of the oven will be fighting against the cold of the interior to keep the meat between at a pretty even temperature up to the edge. IMO you're more likely to get the gray band if the meat is room temperature at the start of cooking, because the center will pull in less heat from the surface, allowing that heat to cook the outermost parts of the meat faster.
So, point #1, just ignore this advice, please. If you want to take the roast out an hour before hand and dry brine it, absolutely do that, and if you want to leave it out or put it back in the fridge during the dry brine that's up to you, it really won't make a difference. Personally I dry brine in the fridge for several hours, maybe as much as 24 for a large roast, and I like doing it in the fridge because it makes the surface nice and dry.
As for the safety issue, at 4 hours out of the fridge you are definitely bumping up against the possibility (even if low) of spoilage on the surface of the meat. And as has been noted elsewhere, this is the kind of spoilage that cannot just be cooked away because the stuff left behind by the microbes is nasty and doesn't get destroyed from cooking. So from that perspective too, leaving the roast out for that long is just not worth the risk, even if it isn't a huge one.
However, I should point out that you seem to also be counting the time while it's in the oven, and I do not believe that is an issue. The concern generally is what's going on on the surface of the meat, which is exposed to air where microbes, molds, etc., live. For a healthy cow there shouldn't be anything nasty living inside the meat which is the very reason we can eat it raw. Once you put the meat in the hot environment, the surface becomes sterilized pretty quickly. Whatever time it was exposed to the "danger zone" temperature before and after cooking definitely counts, but there's no reason it should count during cooking. Otherwise sous vide, smoking and other ultra-slow cooking methods, where the interior of the meat could be spending several hours in the "danger zone", would be much less safe than they are.
For GROUND beef, liquids, mixtures, etc. that is a different story of course, because there will have been exposure to air and microbes throughout the entire volume of the food. But if you're cooking a solid roast for 2, 3, 4 hours or longer in a 200-300 degree oven - or even a whole prime rib sous vide at 125F for 10 hours! - and don't leave the surface exposed to room temperature air more than a couple hours before and/or after cooking you should have nothing to worry about.
