1) Put the thread reply text field at the top of the comments and show new replies at the top, at least for the user who made the comment.
2) Replying anywhere else should require clicking on Reply under that comment.
This makes it intuitively clear that thread replies are not replies to a thread comment.
This would take users some time to adjust to, but should fix the problem.
I know at least one site that does this. Ahem.
EDIT: Looking more carefully at the second screen shot, it looks like they did this. Seems like a non-issue in that case. The first screenshot for some reason doesn't have that change. Who knows if they are A/B testing or what. Strange that the OP did not notice this difference.