Even if you're eligible and you apply, there's no guarantee that your application will get processed or approved. There have been people on the exchanges whose income fell below a certain threshold, so they lost their subsidies, but then didn't have their Medicaid application approved. So they ended up paying more money because their income went down (in an area without the ACA donut hole).
There's also processing time for the application. At least in some states I believe they'll reimburse you if you get approved, but what happens if you don't? Or, perhaps more pertinent to this situation, what happens if you get your new job while you're application is in progress and then have to cancel the application before it's approved?
Keep in mind the article makes it sound like she was actively looking for a job. If you think you can get a new job in a few weeks you probably wouldn't want to get involved in the administrative mess for benefits you wouldn't actually receive.
The ACA has a lot of sharp edges that most people aren't aware of until they run into them. Look up the family glitch and Medicaid churning for a couple of other examples. It's a good example of why universal programs are far superior to means tested programs. Means tested programs often turn into Rube Goldberg messes when they try to cover all the edge cases.