My take is that her support for that dissent is:
1. a player playing the game; above all she wants power/career advancement and by writing that article, she set herself up nicely;
2. more of the same when it comes to the arguments conservative jurists use; when the political end requires it, the opposite reasoning is just as useful.
King v. Burwell is clearly a case about a typographical or drafting error. The idea that a law about expanding health insurance coverage that would allow its opponents an easy way to prevent that expansion, and in a way anticipated in the very text of the law itself, is absurd, and the dissenters know that.* It's also obviously a case about one of the biggest hot-buttons of the era. What side you're on matters most. That Scalia, Thomas and Alito would take the tack they did when the opposite argument has been in their repertoire before is unsurprising. I agree with wildcat's assessment in that neutral, thinking people, should see through both Scalia's dissent and Barrett's support of it. They should see someone for whom the reasoning is just a means to an end. But membership in the 9 (for now) isn't about being a fair-minded jurist. It's about power and priority.
I don't think less of Ms. Barrett because of her support of King v. Burwell. I don't even think less of the state of conservative legal intellectual thought because of that case and its use in subsequent jurisprudential discussion. My regard for the latter went to zero long ago. That Barrett feels she has to play that game to achieve her life goals is all I need know about her. But, of course, my opinion of her doesn't matter; she will be confirmed, and another Alito will occupy the Court for 40+ years. Shit happens, Texas hires coaching frauds and conservatives acquire power however they feel best. So she's to be the Ted Cruz of the Supremes? C'est la vie.
That case does confirm to me that Roberts will likely be, in the main, a fair-minded justice. He's made some rulings I dislike. However, it appears he at least has some intellectual integrity.
.* Scalia has written eloquently and on the limits of textualism, pointing out that when an absurd result is reached, that should not be the interpretation.