DeWeese and Rasmussen on a principle of sufficient reason

In the book In Defense of Natural Theology (IVP, 2005), Garrett DeWeese and Joshua Rasmussen wrote an essay entitled “Hume and the Kalam Cosmological Argument.” defend a version of the Principle of Sufficient Reason, which they call PSR3:

PSR3: There is a sufficient reason why some concrete objects exist rather than none at all.

However, they say that PSR3 is rejected by William Rowe on the grounds that it is not self-evident nor a required presumption of scientific inquiry.

However, they think that PSR3 follows from a weaker, modalized version of PSR:

PSR3’: Possibly, there is a sufficient reason why some contingent concrete objects exist as rather than none at all.

They prove this with this argument:

There is a possible world W in which q is true and q explains p.
p is contingently true and there is no explanation of p. (Assumption for indirect proof).
There is a possible world W in which (p and “there is no explanation of p”) is true, and there in which q is true and q explains (p and “there is no explanation of p). (from 1 and 2)
In W, q explains p, (from 3 and the distributivity of explanation over conjunction).
Therefore in W, p both has, and does not have an explanation.
It is not the case that p is contingently true and there is no explanation of p.
Therefore, it is not the case that, for any proposition p, p is contingently true and there is no explanation of p. (from 6)