Changing PhD programs: should I submit a recommendation letter from my old advisor if it's not purely positive?
Not all cases are equivalent. Unfortunately, switching PhD programs is something that is not often done. This is such an exceptional case, that I think it's one of the few instances in which a purely positive letter from a supervisor is not called for. 

The basic issue here is that the people reviewing your application need to understand why you left the previous program, and be able to judge whether the issues were environmental (over which you had no control, and therefore would be unlikely to be repeated) or structural (likely to reoccur, and thus reducing the likelihood you'll finish the new program). 

Consequently, I would find a recommendation letter from the previous advisor that is only positive highly suspicious. If everything is positive, why are you leaving? Someone needs to explain the situation clearly, and we need to hear from both you and the advisor what each of you believes happened, and why a "fresh start" is needed. If somebody was applying for admission to my PhD program after having started one elsewhere, and if I were at all interested in the candidate, the first thing I would be doing is contact the old advisor to understand why she wrote such a strong letter. Because otherwise the pieces wouldn't "add up" correctly.

Moreover, I don't think you can submit an application for admission to a new PhD program without a statement of support from your old supervisor. If you don't provide a statement from her, it will again look suspicious, and damage your chances of admission. (The person reviewing your application will think: what is this candidate trying to hide?)