I've only begun using Delta regularly this year and have gained access to the CRC with my President's Club pass. However, it is always examined carefully, my boarding pass is requested, and a lot of detail is done on the computer.
As an aside, I had developed good relations over the years with quite a few Pres Club personnel and could get a lot done there, but Cheryl Benz in the LGA CRC trumps all. I've seen her twice, and both times, she got us the best seats on the plane, and would not listen when we said that "our seats are already pretty good." She always has had better, and really wanted to get them for us.