There is an interesting relationship here. Generally, economic signaling models would tell us that consumers should infer that a movie that opts out of a (standard) reviewing process is doing so to escape bad reviews, because the filmmakers know that it is going to get negative reviews (i.e. it is a "bad" film). If it was a "good" film and was thus going to get good reviews, they would let it be reviewed and get the benefits of that. Thus, only bad films would avoid reviews. As a parallel to the standard economic signalling example, what would you think about a used car you were thinking of purchasing if the seller wouldn't let someone examine the engine? That's what's going on here.
However, despite this, some of these films are going on to be very successful at the box office (at least in the first week, which is increasingly the only thing that matters to the studios). So what's going on? Looking at the films that have been successful despite signaling that they are "bad" films, my instinct is that this is precisely the move they are looking for. The audiences for these films are likely to be made up largely of consumers whose tastes are negatively correlated with the tastes of film critics, so by bypassing the NY Times review (and others like it), the film makers are precisely signalling that critics won't like this (but you will) and instead are focusing on using word-of-mouth and TV advertising to reach out to their intending audience. And they do this without the cost of screening films for critics, and by postponing the negative reviews until after the opening weekend returns are in.
Since studio executives greenlighting their projects are likely to base their opinions of the film makers both on reviews and performance (although ultimately caring only about performance), there's a clear benefit to getting good performances to them before the negative reviews do. That way, you avoid a week where your studio head thinks you've created a bomb, before having performance data to demonstrate that that is not the case. Instead, you have the #1 box office ranking in hand, and the negative reviews are never considered.