Unfortunately (as per the article), there is precedent for someone getting a DNR tattoo as a joke after losing a bet in poker.
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.