Assume Alice authenticates a message $M$ with nonce $N$ and secret key $K$, creating authenticator $A$. She then sends $A$ across the network.
The Poly1305 paper does not seem to specify whether it is possible for an adversary, whom has seen $A$, to determine whether $A$ is just random bytes or has characteristics of an output from poly1305.
For someone interested in deniability, this is an important distinction. Are poly1305 authenticators distinguishable from random data?