I've never heard anything about refusing to pull unsafe equipment. Dispatch either tries to get it fixed or swings it to another door. One time my trailer was 100 pounds over on the drives and I made them rework it because I was going through areas with scales. They weren't happy, but they did it and I never heard anything about it after the initial complaining.
On a weekend run I refused to pull a trailer because it didn't have an inspection sticker. Called Central and they were cool with it and updated the trip to a single and have me 30 minutes delay pay.
Our health insurance could be better, but after enough time on TB, I've reconsidered my Union position because the union shops share the same issues we do, just with better health care. Local management is going to do what local management does regardless of union presence.