Why would either need to be involved? Are you telling me that ALPA will control the training department and how ckeckrides are conducted?
Many MECs have a Pilot Training Review Board and a Training Committee that works with the company on establishing standards for how training and checkrides are conducted. Checkairmen that are consistently causing problems are dealt with, a "training footprint" is established that lays ground rules for what sort of training you'll have to do for busting different events, etc...
Also, most agreements give you the right to refuse a certain checkairman, and also give the right to have a union representative observe your ride.