But it is what it is. Your mother has breasts, you didn't. So, you are not like your mother. There is no reason to believe that your DD will develop like you did. I think you need to tell her your truth.
The 25' guideline from http://www.safetycops.com/grill_safety.htm comes from police officers. Who would, I assume, have no more expertise on the subject than anyone else.
Most people I know, have their grills within five feet of their houses.