Ask HN: How would GDPR apply to dual citizens?

Let's say I'm a citizen of America and England. I go to a site, and they collect my data. I later send said site a GDPR notice demanding they delete my data. The company fires back, claiming that I accessed their service from a US IP and so accessed it in my capacity as an American citizen. I claim I've accessed it as a Brit.

How would this go down in court?