Unfortunately, this isn't true with regards to the NAAT test on day five. I confirmed this with the public health department yesterday via an email exchange.
I also confirmed that the test is free if done at the health department, but it can be done via a private testing company at the customer's expense. We'll have to see how it goes once the new program goes into place next week, but some visitors may opt to spend the $125 out of pocket in order to not deal with what likely will be a clusterfack at the health department when 300-odd Americans all have to get tested Thursday of every week. My wife and I are trying to decide if we want to pay the extra $250 plus whatever location fee a private company charges (it's $120 for Bon Bida Bonaire to do it, split amongst however many people want to go in on it) or do it for free and deal with the wasted time. Since we already have to get an antigen test at $25 each to return, that's $50 versus $300+.