I'm not quite sure how you think this would have anything to do with the US, but I believe (based on previous posts) both those folks made platelet donations. That is a much much more involved process requiring a larger gauge needle, hence the larger bandage.
http://www.redcrossblood.org/plateletFAQ
Wow -- a platelet donation takes so much time - and both arms! But it wasn't a large needle when I did it - it was actually a lot smaller than the regular donations.
I'd really like to do plasma donations. Although my whole blood is of limited use, AB plasma is the universal donor. It's just a bit of a struggle to do as there are limited sessions here and it takes 3-4 hours.