Covariance, stochastic discount factor (SDF) and risk aversion

The Euler equation is $$p=mathbb{E}[MX]=mathbb{C}text{ov}(M,X)+mathbb{E}[M]mathbb{E}[X].$$ If the payoff $X$ doesn't covary with the stochastic discount factor (or pricing kernel), then it does not have systematic risk. Because $mathbb{E}[M]=frac{1}{R_f}$, where $R_f$ is the risk-free rate, you indeed obtain $$p=frac{mathbb{E}[X]}{R_f}.$$ As you see, you compute the (real world) expected payoff and simply discount at the risk-free rate. The agent's utility (be it time separable, recursive or whatever) and risk aversion does not enter the pricing formula.

Remember that in the CAPM only comovement with the market (as measured by market beta) is priced. Well, in the CAPM, the SDF is a linear function of the market returns. Thus, the same intuition applies here: if the payoff of your asset doesn't covary with the market ($beta=0$), then the risk-free rate is the appropriate discount rate -- regardless of potential idiosyncratic risk. Only covariance with the SDF (market) is priced.