Eugene, here is the test page I’m working with.
http://www.test2.indianaskywalker.com/
I get the same problem on my regular site. If I enable the comments for my posts then I get the “Leave a reply” section at the bottom of my recent posts page. Even if I disable the comments for the page. I’ve tried a number of different combinations of things including using the comments plugin that I have. But at the end of the day if I disable all comments on the page but enable comments on my posts then a reply section shows up at the bottom of my recent posts page. The reply format is not a format that I am using though, I don’t know where its coming from. But it only shows up when I use your plugin.