vision - Why do objects of a given color appear white under light of that color?

Under light from the sun, a red object will scatter the red component of light, and absorb all others. Hence, the human eye perceives it as "red". White objects scatter all wavelengths of light.

Yesterday I bought an orange light bulb. Under its light, orange/reddish carrots look white. Why is that? A "white" object would have to scatter all wavelengths of light, but there's only red light to begin with.

Here's a photo of a person's hand, in white then in red light. Notice the color of the red nails. Do they appear white in red light, or does the white skin appear red?