The security of Hidden Field Equations - sentence
Random oracles are used in cryptographic proofs as a way to abstract away a complex function, making the analysis easier (ie "ignore the actual function, and model it as a random oracle instead").

In the paragraphs before the sentence you highlighted, they propose to measure the "complexity" of an equation / function by the degree of its multivariate polynomial representation over $GF(2)$.

In the context of the surrounding paragraphs, I would interpret that sentence to mean


  The random oracle paradigm abstracts away the complexity of the function, which renders our complexity metric useless.