Do The Lost World & Jurassic Park III still work with Jurassic World?

G. H. (Gman)
AdminTyrannosaurus RexFeb-13-2016 9:27 PMI've been rewatching the entire Jurassic Park series lately and wrapped up The Lost World tonight. (Still a wonderful move and still my #2 in the franchise.)
Now lets keep in mind that in April of 2015, Yahoo Movies reported that Colin Trevorrow's Jurassic World was more of a direct sequel to the original film and didn't acknowledge the events in the sequels. This same article tries to clarify that The Lost World and Jurassic Park III haven't been pulled from the continuity, they simply aren't referenced in Jurassic World. The mention is still vague. Here's the short excerpt from Yahoo news:
"According to Trevorrow, the previous sequels aren’t being written out of continuity so much as placed to the side, as they both unfolded on a different island." - Source
So lets go ahead and assume that Jurassic World's universe includes the events of The Lost World and Jurassic Park III, regardless of the movie's philosophy toward them. Other than the logic flaw of okaying a third attempt at a dinosaur theme park, how are some of these animals still alive? How are some of the ruins of the original park still standing?
It's heavily suggested in The Lost World that Ludlow and InGen covered up Isla Sorna and the animals on the original island either died or were slaughtered. The original Lost World VHS summary reads, "The dinosaurs are destroyed, the park is dismantled and the island is indefinitely closed for the public..."
While I can't consider a VHS summary cannonical it does seem to hint at the deleted scene in The Lost World where Ludlow is listing the money InGen has thrown down to keep the island under lock and key. In this cut footage Ludlow mentions "biological" evidence being destroyed--Whether he's refering to dinosaurs or other biological experiments is unknown. However, I think it's logical to assume that killing the dinosaurs would have been an obvious step in covering their tracks.
Then of course there's the curious line John Hammond utters in the theatrical version of the The Lost World, "Thank God for Site B." Why would he be so relieved about it unless everything on Nublar were destroyed? Why not send a team to Nublar if the animals did survive? Or two teams on both islands?
Or am I looking at this wrong? Rexy's survival seems to indicate that she, among others, might have been re-captured for Jurassic World's rise. Is it possible she's one of the few and maybe only survivor of InGen's purging? Even if she did find a way to allude them, what kind of food source could have possibly sustained her?
While I understand Trevorrow's desire to pay greater homage to the original movie instead of the sequels, pushing them "to the side" just because they take place on a different island ignores some greater parts of the mythology--Especially if they are still to be considered cannon. It makes more sense if The Lost World and Jurassic Park III are not cannon, but that has never been confirmed. Nor do I think those two films should be ignored as neither merit a badge of dishonor so great as to be removed from the mythology.