They are not going to go horizontal just to get under your land and screw you. They are going to do it because they can cover much more land with only one well. Horizontal wells are surveyed, and the oil companies know exactly where the wellbore goes. These surveys are also turned into your state's department of natural resources. From what I have read, it looks like the company wanting to drill on your land is planning on drilling one lateral wellbore per section of land. Therefore, if you do not own that entire section, the well will be drilled on more then one landowners land. Once this happens, you don't get to call the shots. It is between everyone who owns that section of land. Say you own one quarter of the section and the section gets leased out at 17% (1/6). You would get 4.1% of what that well produces.
I am no lawyer so I can't guarentee everything I just said, but I have a fairly good grasp on how this works.