Short answer: It's probably 0.6 because that's what the algorithm says it should be. Why the algorithm says it should be 0.6 is up to you to figure out.
Long answer: I looked at the MATLAB documentation and I see the 0.6 factor you are referring to. As you already mentioned, there is no explanation for this listed. However, the MATLAB documentation does mention two journal papers by Jon Dattorro at the bottom of the page (down in that References section that I usually, and you possibly also, typically ignore). If you were to look into the first of these papers, you would find the same 0.6 factor is listed in the original author's pseudocode, in Table 2. I would guess MATLAB is just implementing this code as-is. Since the paper says 0.6, MATLAB makes it so.
With no knowledge of any of this, I tried scanning the paper myself for a better answer, but I don't see an obvious reason for the number jumping out at me. If you need a better answer, I suggest you, with your expertise in this area, start by reading the paper yourself and see if you can find a better answer. Note that it's possible the author has pulled that 0.6 factor from yet another paper and simply referenced it without sufficient explanatation. In that case, you would need to track down that reference and read that paper. I don't know how deep the journal-paper-reference hole goes, but this should be enough to get you moving toward a more satisfactory answer, if "because it is" isn't good enough. If you do figure it out, feel free to come back here and answer your own question with what you find out in order to make the path easier for others. Alternatively, you are also welcome to try contacting the original author directly with your question, as he may be happy to help you understand why he wrote it that way. Either way, the next step seems to be outside the scope of MATLAB and MATLAB Answers.
If the factor is indeed arbitrary, go ahead and submit a bug/feature request to MATLAB with your explanation and references. I'm sure they can make it another property in the reverberator object for you to adjust, with 0.6 being the default value.
