Swap Rate Curve

Hello Everyone,

I think I am not getting the mechanics of the Swap Rate Curve. So in the Term Structure reading they derive the Swap Rate curve using government spot rates (example 8 pg27). So, since they are effectively discounting cash flows at the risk free rate, does it mean that the swap rate curve which consists of the swap rates, represents risk free rates? And if so, this sound to me like we are effectively solving for the government par rates, since we are solving for the payment (=swap rate) that makes the fixed rate leg to equal 1. Also, if the swap rate curve is a risk free one, what kind of risk does the swap spread reflects? Or we are only calculating the swap spread for risky counter-parties in the swap contract? I am not sure, maybe I am mixing things up, any ideas?

Many thanks