Disability is a necessity if she cannot maintain living on her own, as one day she will not be able to depend on others for an income.
Seeking help doesn't necessarily mean she had to apply for benefits or disability.
Constant over-relying on family for survival is similar to an inter-dependent lifestyle on disability.
There are online groups therapies, and many cities have free clinics.
If she gets a job, she can afford slide-free counseling and group meetings.
With therapy she may improve vastly, and currently the consensus is that some people may even completely recovery from mental heath issues in the future, and seeking help now is a possible step in that direction.
In regards to employers looking at mental health records, most cannot because of HIPPA Laws. It is possible that government employers may have access to those records, but the government only employs 1% of the U.S. population, so it's an unlikely path. Even if, people can fully recovery from illness [stranger things have happened], and if people can prove to authorities this is indeed the case, their official medical records can be challenged and expunged [again, rarely has anyone ever taken this route, and those that have don't speak about it].
If your sister is still adamant against applying for benefits, I would lay out all of the advantages of the system, such as subsidized housing costs, subsidized health care, freedom from illness inducing stressful lifestyles, etc.
If all else fails you could convince her that she could use the system against the system by using the money otherwise going to the wrong areas, she could then funnel it to whatever area she saw fit.