He's right... explains it perfectly, at least the theory.
Not all wheels are cone shaped enough that you can see, but they're supposed to be. Use and wear will flatten them out. Same thing with rail, it wears, flattens and at times doesn't maintain the profile that assists that transfer. Machine shops can rebuild the wheels once it gets worn out, by welding up, them machining down the surface and restoring that tapered wheel.
We have a grinding train that comes to each territory in a year and re-shapes the rail to the profile that it's supposed to be. It helps the rail in the curves last longer and assist that process as explained in the video. The grinding train is a massive, dusty, spark-creating mess that sets fires as it works. I was on the grinding train this Spring, working nights so we could see the fires easier. They actually have infrared cameras onboard, to find hot spots.
Curves wear much faster than tangent (straight) track. I should pull up a photo of some well worn curve worn rail, it would probably scare the hell out of the guys that operate the trains to see what those curves can look like once the ball (top) of the rail gets worn down.
There are actually 'greasers' or lubricators installed into curves that are VERY important to keep the rail and train wheels from wearing and to prevent the wheels from climbing the rail and derailing the train. They're messy and require a lot of maintenance, but save lots of money when they're working. There was actually a derailment on the neighboring section of track here in Colorado that was caused by the lack of grease in curved track a couple years ago.
Here's one more small mind-bender for ya.... rails are NOT laid straight up and down. There's a small cant, tipping the rails inward, towards each other, which helps prevent the rail from rolling out under the load of a train.