I disagree. By all indications, the DOT has authority to regulate behavior occurring in the US. And customer service matters pertaining to travel in or via the US are well within the authority the DOT has long enforced.

The DOT has numerous rules that explicitly regulate the conduct of foreign air carriers when they serve the US. See e.g. the Notice of enforcement policy: oversale notice for foreign carriers. By its plain language, this rule covers "foreign air carriers", and nothing in the rule suggests that this rule benefits only passengers originating in the US.

Analagously, many folks here may be familiar with EU rules on air travel disruptions. Those rules benefit even non-EU citizens when flights arrive, depart, or connect in the EU.

Nothing of this offends my sense of extra-territorial application of law.