Both sides of the card have to fit the color identity of the commander.
The identity on the flip side (the back) is the color border.
Okay, so you're right, but for the wrong reason.
I dug through the rules (I'm bored,
hush), and 202.2 says that "An object is the color or colors of the mana symbols in its mana cost, regardless of the color of its frame."
However, digging deeper, 202.2e says "An object may have a color indicator printed to the left of the type line. That object is each color denoted by that color indicator. (See rule 204.)"
204 is
204.1. The color indicator is printed to the left of the type line directly below the illustration. It consists of a circular symbol filled in with one or more colors. A color indicator is usually found on nonland cards without a mana cost.
204.2. An object with a color indicator is each color denoted by that color indicator.
So each flip side had a colored circle on the left side of the type line (
unhallowed cathar, for example, has a black circle.) Elusive mist has a blue circle in the spoiler, so unfortunately it won't fit in my deck
Apparently the color of the border could, in fact, differ from the card's color alignment. I couldn't find an example, though.