Upvote:3
The article you refer to is bylined “Kiwi journalist Lisa Scott”. The VWP is not available for work as foreign press, radio, film, journalists, or other information media so it seems Lisa should have been very careful and, it seems, may not be presenting all the relevant facts to readers (or to Immigration?).
She stated Applying for an ESTA after starting with a J-1 was illegal.
Exchange Visitors cannot travel on the Visa Waiver Program or with Visitor Visas (their emboldening, ibid.) and “All exchange visitors must travel to the United States with exchange visitor (J-1) visas.”
We don’t know timings, but if you intend to extend your stay beyond 90 days or change your status once in the United States (for example, you intend to request change of status to student or temporary worker, etc.), then you need to apply for a visa.
Timings are also relevant because a J-1 application requires submission of a Passport valid for travel to the United States and Please note that exchange visitors beginning new programs may not enter the United States more than 30 days before their program start date.
Is it actually illegal, or what else might she have done wrong to be told this?
Yes, and there are various possibilities.