> . This tattoo does not hold the same weight as a donor endorsement on an ID, even though it says exactly who to contact.

The tattoo wearer in this is explicitly saying that he is not ok with donating anything other than to the two listed organisations. Donor ID would not be appropriate in his case.

For example, in the UK the law is under the Human Tissue Act 2004, written and witnessed consent for anatomical examination must be given prior to death. Consent cannot be given by anyone else after your death. A consent form can be obtained from your local medical school and a copy should be kept with your Will. You should also inform your family, close friends, and GP that you wish to donate your body. 

Note that you don't have to have a donor card on you, because donor card is not for giving your body to science, it is for giving your body to medicine, something the hospital would have to directly act on.

If you want to donate to a specfic scientific research group, you have to register with them so they can prove they have a right to your body (and for how long, many people only donate their remains for a limited period of time). A donor card cannot cover this.