No. "near-infrared" isn't a red color shade, in fact it's not normally visible at all. Near-infrared is what your media remote uses to control your TV and audio system. You really cannot see it.
Huh. No, I can definitely see it. I just looked at my HTC One's IR transmitter for the first time, without knowing where the LED is. It's pretty clearly on the right side of the lock button, just under it.
I don't have HTC One to make a comparison - but if you have some "vanilla" remotes laying around and can see the IR LEDs blink in all of them when active - then yeah, probably you do see into the IR and I don't!
Yeah, I just tried both TV remotes (one is just a Samsung remote). I can see all of them, but it's only a faint glow. Try it in a dark room, you should be able to see it.