This is something that virtually all dogs love or would love to do if and when given the opportunity. If it were the first time she was allowed to go off on her own, such personal guilt might be understandable, but in this situation no blame or fault is justifiable. In times of loss, our souls struggle to make sense of situations. All too often raised to assign blame and fault to things, whether to ourselves or others, we often miss the mark. Regardless of what mysterious chain of events transpired to end this dog's life, that is now in the realm of history.
Nothing can change it.
The only thing that matters now is what you do about it now. I think not. What lives on is the love you shared, and this is what must be cherished and held above all else. Yes, mourn her physical loss, but celebrate the love you shared which will forever have its place in your heart. And be thankful that you have good friends who are willing to share your pain and extend their help and support in times of need.