I was reading this article where the author claims she was told it is illegal to obtain an ESTA while you are in the process of applying for a J-1.
However I could not find any online information to confirm or deny that, and in fact one US gov site says that it is OK (and in fact, required) to enter on an ESTA if you also have a J-1 but you were making a recreational trip.
Is it actually illegal, or what else might she have done wrong to be told this?
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.
and in fact one US gov site says that it is OK (and in fact, required) to enter on an ESTA if you also have a J-1 but you were making a recreational trip.
This is correct. A J-1 visa allows you to apply for admission only to participate in an approved "exchange visitor program." You cannot use a J-1 visa to enter as a tourist or as a business visitor; for that you need either a B visa or, if you're eligible for the visa waiver program, a valid ESTA. By contrast, a valid ESTA does not allow you to enter as an exchange visitor, which explains why the author of the cited article wasn't admitted to the US.
It is not generally illegal to apply for or to use ESTA if you have a pending application for a J-1 visa. For a separate trip that has nothing to do with your exchange program, in fact, ESTA or a B visa (or whatever visa applies to the independent reason for this separate trip) is required.
