I hate where I am going with this, but it is possible they are interpreting as follows:

If you HOLD a US/UA *G card, you are not allowed access even if that is NOT the card you are using! Just the fact that you have the card means that you are not eligible. While this is insane, it seems that the way the policy is worded, such an approach could stick.

The OP referes to this sheet of paper - did they give you a copy? If so, could you detail its contents and if not, do you remember what it said in more detail?

I have just emailed 1KVOICE - perhaps we need to start a real campaign of emails on this ASAP.