The mathematical result I think you are referring to is: any uniformly distributed random variable xored with any other independent random variable yields a uniformly distributed random variable. On the other hand, if we take the strongest random source in the universe, say X, and xor X with itself we get:

X xor X = 0

The result is just a sequence of zeros, which is not "as strong as the strongest source". In practice, people may take lots of different "random" sources as input to their random generators to make them "more" random. But if you don't take care to check if they are independent, you may have a problem.

On the contrary, the above computes exactly the identity cipher: your "ciphertext" is your plaintext.

Mathematical results will lead you to surprising conclusions if apply them in the wrong context!