I see you're right that the word "manipulation," isn't used. I actually thought it was, based on conversations I've had with psychologists. I believe the inference of "manipulative," is made from some of the following:
"Frantic efforts to avoid real or imagined abandonment," efforts which may often involve manipulation.
"Recurrent suicidal behavior, gestures, or threats, or self-mutilating behavior," all of which is inherently manipulative when done in the context of a relationship.
"Inappropriate, intense anger or difficulty controlling anger," which often results in manipulation, overt or covert.
"These abandonment fears are related to an intolerance of being alone and a need to have other people with them. Their frantic efforts to avoid abandonment may include impulsive actions such as self-mutilating or suicidal behaviors . . ."
I'm quoting the DSM V, but there were no significant changes made to this disorder between IV and V.
"They may idealize . . . at first or second meeting, demand to spend a lot of time together . . . however, they may switch . . . feeling that the other person does not care enough, does not give enough, or is not 'there' enough. These individuals can empathize with and nurture other people, but only with the expectation that other person will 'be there' in return to meet their own needs on demand."
There's more but I'm tired.
After hearing for years about how cunning and manipulative people with BPD are, it's very interesting to see many people here say the opposite.