Korban Chatat

Zahava and I were assigned to the korban chatat. As we were reading through the pesukim, I noticed something very strange.
The first case of a sin offering is when a cohen sins and it results in the guilt of the people because they are dependent on the cohanim to atone and pray for them. The rest of the cases of the (non-cohen) Jews basically have the same procedure of bringing the korban chatat as the cohanim. This is where I become confused. The cohanim are on a much higher level and are the leaders of the nation. If so, why then is their 'punishment' the same as the rest of Bnei Yisrael. We learn throughout the Torah that in general leaders of the nation, like Moshe, usually get a harsher punishment than the rest of the people. For example, Moshe hits the rock so he can't go into the land of Israel?!? I know that bringing a korban should not necessarily be classified as a 'punishment,' but shouldn't a cohen have to go through a more tough procedure than everyone else? Also, these cohanim are the ones atoning for the rest of the nation's sins when they bring korbanot, so surely a cohen's sin should be dealt with in a more severe and stringent way.