Is it true that it's ok to donate blood with an open wound?

Unrelated: Donating blood is an extraordinary gift from a person to help others. To protect the recipient, a lot of testing is done on the blood to prevent transmission of certain bacteria, viruses and other things in the blood. The mere presence of a wound has no effect on the blood itself so if you had anything as simple as a shaving razor cut to a big wound, it would not affect the blood for donation.