Hell, just transmitting large blocks of 100% mathematically random data is a red flag. "One-time pad in use! Something very interesting going on here!"
In theory, there are three things that are 100% mathematically random:
1) Random data, such as the output of a hardware random number generator.
2) Encrypted data. One of the criteria for an encryption algorithm is that the output is indistinguishable from randomness. If you can tell the two apart, you can gather information about the plaintext.
3) Compressed data. If you can tell it from a stream of random bits, that represents a redundancy you can use to compress it even further.
In practice, you can tell the three apart, because compressed data usually comes with a header or other uncompressed structure, and almost nobody sends large random numbers around.