When you load your digital card on the
DVC website is it the regular blue card or the white one that says it's only eligible for TOTWL, pool hopping, and DVD rentals? That is how the discounts are supposedly to be administered since they have no access to a database to check eligibility. As far as the discounted AP and gold AP go MS will not sell you one without first checking to verify you are eligible. When you go to activate it they also require you to supply the card. I would assume if you try to show the white restricted card or no card at all they will deny you.
As far as the restaurant discounts go I've had them Given to me when I was wearing my DVC slider on my magic band a couple times without being asked to see the card and my ID. Merchandise locations have also asked to see both.