I've heard that there is something on the paperwork that you mark to have them throw the blood away. For example, say you have HIV and your work is doing a blood drive. You are pressured to donate, but don't want to reveal that you have HIV. So, this way you donate, but you mark on the form that they need to discard your donation.
I've never donated blood, so I'm not sure what all paperwork is actually involved. I used to donate plasma, because there was a place in town that paid you for it, and your body replaces it much more quickly than blood.