How much less common? Again, have you seen any actual evidence that P-P fusion events actually happen in actual Earth-bound plasmas? Because the numbers I've seen indicate that at Earth-bound plasma densities, such events are so unlikely that we should not expect to have observed any.
PS: And thanks for this, it's good to be called out on something like this. I tossed out the PP comment without thinking though simple contamination is a far larger source of high energy neutrons.
It looks to me like the comment about the rate being too small to measure in the lab applies to the PP fusion into deuterium; that's the reaction referred to in the statement you quote. The positron that's produced is not a "beta-plus decay of deuterium"; it's a product of the PP fusion into deuterium, part of the same overall reaction.
As to PP fusion from what read. Without a large enough plasma the beta more common proton emission path >99.99% ends up costing more energy than you gain from beta-plus decay <0.01%. "The least stable is 5He, with a half-life of 7.6×10−22 seconds, although it is possible that 2He has an even shorter half-life" http://en.wikipedia.org/wiki/Isotopes_of_helium#Helium-2_.28...