Yes, but they turned a blind eye to leadership's political actions, greed, corporation bashing, quality issues and uncompetitiveness. They're complicit.
Things are more complex than that. The UAW has elections, and much like US elections, what the candidates say they will do is often different from what they actually do.
Regarding quality issues: I can assure you that the guys on the line - at least the lines I was involved with - took a keen eye on quality issues. It often got to the point where if a supplier - manned by fellow UAW workers - were supplying bad quality parts, the workers would get together to write protest letters to their brethern at the supplier. They realized their jobs were on the line.....
Do all situations at UAW plants work out like that? No. Were things perfect? Hell, hell, hell no. Were there bad apples? Hell yes - in both management and union.
But still there are good people there too - and they don't deserve the broad brush being applied in this forum. It's like bashing California, home of the Robinsons and the FR server (as well as a lot of good FReepers like yours truely....)