Yes, that's exactly it. As an S-Corp the corporation doesn't pay any taxes. Well, in my case my state (New Jersey), has a minimum tax based on revenue. I pay that, but it's minimal. If it really bothered me, I could re-incorporate as a Delaware or similar LLC. All profits are passed to your individual return and you pay taxes on that.

With the K1, you will be adding the passed through income to your personal income and still paying tax on it. I'm not seeing the benefit of an S-Corp here.