research level - Does recent paper show Bohmian mechanics is correct?

The following paper was recently featured in a German science magazine (Spektrum der Wissenschaft): "Experimental nonlocal and surreal Bohmian trajectories" (DOI:10.1126/science.1501466)

The abstract reads

Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.

To what extent does this show Bohmian mechanics is correct in the sense that it explains things normal QM does not explain?

Unfortunately I had to realize I don't know enough about the subject to understand the full paper. I would just like to know if they actually claim to have experimentally shown that an interpretation of QM is distinctly different from standard QM.

I am particularly asking in light of thoughts like this.

EDIT

I first accepted the answer given by @Timaeus below. There are two reasons I removed the acceptance tick again:

1. I discussed with a friend who knows a lot more than me about weak measurements. He said they are not really completely understood yet, nevertheless give surprising empirical results. These seem to be hard to reconcile with the standard interpretation of quantum mechanics, though a lot easier to reconcile with things like Bohmian mechanics. It is hard to read from the papers if it actually shows distinguishing features between the interpretations. Now Timaeus argued that they can't because the "interpretations" by definition only predict the same results. Well, apparently they don't so I will repeat my question slightly differently: Does this paper show that Bohmian mechanics is correct and that the standard interpretation is not?


2. There has been another recent paper by the same group that in fact won the "Breakthrough of the year" award. From the abstract:

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.