In general, I try not to use internet JPG images to discuss colors, but it's pretty tough to discuss colors on the internet without using images. JPG is a lossy compression format by its very nature and, furthermore, computer monitors simply can't display all of the colors that are visible to the human eye - the technology is just not there yet. Plus, since I don't know what your computer monitor settings are, it's hard for me to guess which colors you might be seeing and which ones your monitor is simply not capable of displaying. I'm using AdobeRGB on my monitor here, FYI, so if you are using sRGB, then you are missing out on a few colors.
So what feels right to my eyes in the real world is going to be pretty difficult to illustrate accurately using internet JPGs. I can just say that when I display the figures and look at them from across the room, the brown bandana just feels more correct.
I did come up with this comparison image and tried to match to colors up as close as I could. I sampled multiple photos for each color and came up with an average, then adjusted that average until it looked right on my monitor:
When I sample the colors using the HSB sliders, I get:
Brown: H = 34, S= 45, B = 24
Red: H = 12, S = 89, B = 54
Actual: H = 1, S = 68, B = 40
So, using these colors, the red clearly is closer to the proper color than the brown. Even though both red and brown bandanas are too far over to the red/orange side of the spectrum and the actual bandana is more a pure, middle-red.
But again it's about how it looks to my eyes in reality. Even knowing what I know about the numbers, the brown just feels closer to the correct color than the red.
Most likely it's because I've spent over 20 years drawing stuff primarily in pencil, so my mind has been conditioned to translate everything into a grayscale image and decipher every color based on it's value first, hue second and saturation level third.