I have experienced this problem as well. If you look at the edit-comments.php file you will see that comments can be edited if the user level is greater than that of the author of the post or if the user is the author of the post. But somehow this gets ignored and edit links appear on the comments section for users of the same level (even level 1). A friend of mine has managed to overcome this problem by disabling the edit comments function, thereby only allowing follow on comments to be added. If anyone finds out why users of the same level can edit each others comments please let me know. Thanks.
