Would you say the same thing about a 10-year old signed card in their wallet?
That said, there are lots of situations where I think it would be stupid to have "Rape Me" tattooed to my body. It might have lots of calligraphic merit, but if it's on your face, you probably aren't going to be working the customer service counter at Target.
Let's say that you are unconscious and stopped breathing.
Your brain is deprived of oxygen. Within 3 minutes, the brain cells will start dying and you will suffer irremediable permanent damage, within 10 minutes, you will be effectively dead all things considered.
What do you do? Do you look for a wallet and the cards inside it?
https://link.springer.com/article/10.1007%2Fs11606-012-2059-...
This implies that people getting tattoos do not treat them as legal documents.
The doctors in this more recent case were justifiably cautious - they did the sensible thing, which is to consult an ethics/legal specialist ASAP, and then follow their advice.
You can assist them to suicide in certain jurisdictions, if they want to end it.
It's pretty hard to resuscitate back to life after they've been dead, and put in the freezer for half a day.
The ugly fact is this comes down to a pure legal choice: Was the appropriate legal work done for the DNR? If not, ignore and save them. A live person dealing with legal is better than a dead person's family dealing with legal.