The Adventura storyline reminds me of Mission: Space's storyline. Going for a simulation because that would be more "believable" than an actual space flight.
Imagine if New Orleans Square had this kind of convoluted backstory to ease our minds about how the French Quarter could possibly be in Louisiana and Disneyland at the same time.
The difference is that New Orleans Square isn't going for a realistic representation of one specific location...it's going for an idealized version of New Orleans from a certain time period. Jurassic Park's (the film's) most endearing quality, besides visual effects, is that it established a very specific and well-realized location. Jurassic Park wouldn't be as effective on some random island--we, the audience, identified with the backstory and the location, all planned out very well by Michael Crichton to be believable. The film established several visually-striking landmarks meant to leave impressions with the audience, such as the Welcome Center, the gates, the Jeeps, the T-Rex exhibit, the raptor feeding-enclosure, etc. The atmosphere created in the film was extremely impressive, with filming done on location in island/tropical settings so the audience truly believed Jurassic Park was on an island, and that this premise could be believed for two hours. That was the movie...
Now we come to the theme park. It's impossible to recreate everything audiences remembered from the movie. Could they build a Welcome Center to the same scale, with the same interior design? No (they couldn't even fit the DNA ride in it). Could they accurately bring the T-rex/velociraptor feeding exhibit to the park considering what room they had? No. Could they have the iconic Jeeps passing by the Welcome Center and navigating around the island? Apparently not. What they could do was recreate a tropical setting the best they could (though they couldn't effectively sell to guests that they were near Costa Rica). So, the way I see it, IOA did the next best thing--they took landmarks from the movie that were decently familiar (a revised Discovery Center) and applied the same general aesthetic without recreating the film entirely, a measure which would have been incredibly costly and impossible considering guests' thorough knowledge of the wonderful atmosphere the JP film created. In doing this, they didn't sell you some cheap knockoff of Isla Nublar, which everyone would know was off...they told you that it was InGen's second try; that way, guests wouldn't be offput by the fast food restaurant inside the Discovery Center, or the huge Environmental Systems building that had boats dropping out of it, yet no Jeeps. It allowed them to be creative within the realistic confines of a theme park (especially one as small as Islands of Adventure) without having to adhere exactly to the films, which is what guests would've asked for.
New Orleans Square is a mesh of several elements of New Orleans in one small and immersive footprints. There was not one specific location within the city they had to recreate. Jurassic Park is a film setting that a lot more people had a better understanding of than a sprawling town. Instead of just giving us an abbreviated theme park version of what Spielberg, Crichton and Co. had established very fully in their film, they went through the trouble of explaining why some things were a little different. This had the bonus affect of being true to the continuity of the series, so instead of believing we're visitors at Isla Nublar (which clearly was shut down before being open to the public), we can believe we are in John Hammond's next attempt. I think it's theme park storytelling at its finest, really.