They can certainly stand on their own.Knowing both helps understanding though.
For example we have Malcolm the Taurus, who is quite a bit more dynamic than the typical Bull. Now we know he is a Tiger, and a Fire Tiger at that, which livens him up a lot, and makes him much more of a roamer. Bulls tend to stay in one pasture, but Fire Tigers are perpetually on the move.
Malcolm probably experiences a conflict between these sides of his nature, and his life will challenge him to follow both these natures. Now if he were a Taurus Ox, he would pretty much be set chewing his cud and I dunno he would ever have been on Survivor.
Brandon is a Libra, like his uncle Russell. Dynamic, lively mind, a certain charisma, mischief maker, social, and so forth. Well, Brandon certainly has the scales always tipping up and down thing going on. But with the Sheep nature, we see where he is very conflicted and emotional.
Note: the Chinese sign we have more completely, because with the Western we are missing the Ascendant. The Ascendant is the persona, the mask we don to present ourselves to the world.
For example, as you noted I am and confess to be an Aries Sun with a Scorpio Moon. My rising sign happens to be Gemini. So a lot of people see the love of too many words, desire to teach, analytical Mercury-ruled side to me and wouldn't know about the Mars/Pluto side. Which is considerably less cerebral and is certainly not diplomatic (Aries is not) or dispassionate (Scorpio always passionate). Because of the Gemini composure and the site moderation, you don't normally see the nuclear explosions constantly going off. At least, not MOST of the time, only once in a while when the Gemini lid gets blown off by the proverbial last straw.
With the Survivors, we are missing that all important piece in most cases. If their personalities seem a bit of a mismatch, remember that the "mask" is the Ascendant, which is the face they aim to show. The Sun and the Moon are the real nature of the self. Survivor tends to strip people down to their core, so the sun and moon signs really are useful.
Oh, and Georjanna, of course you are both a Horse by Chinese and a Centaur (half-horse) by Western, so Horse it is!
I'll let you guess my Chinese sign. It's not too hard if you know me.