Well I can only speak of my own experience but I have been to a 28 day program that did not include detox. They send people to an outside hospital or you can detox in your own way, then arrive at the rehab. They just have to 'clear' that you are out of any danger as far as DT's go. And yes, my insurance paid for it.
Have you called your insurance company directly? They usually have a resource for drug and alcohol dependence, usually under the mental health umbrella. They can tell you exactly what rehabs they are contracted with in your area. You can also tell them that you don't need to be medically detoxed but that has no bearing on the fact that you are addicted and need help. If anything, this will save money as detox is generally the most expensive part of rehab. Finding a facility that does not medically detox is possible. I have also seen rehabs that take people in, whether they need to detox or not, and put them on detox protocal....which is criminal in my opinion. But, that's another discussion.
This is the second thread I've seen about this. Believe me many rehabs won't take you IF you're drunk...so you should be able to find something.