I thought that might be
the "reasons" your wife was using, That's why I pressed for a answer!
The "minimal amount of soap" is a rather tricky question! The first thing to consider is why your using a "soap" or "detergent" in the first place!
The answer is that both are surfactants (surface-active agents) They both reduce the surface tension of the water. In other words they make water wetter, and they both soften the water, witch allows for the shifting of soil in the fabrics. (very short answer really) It gets very complicated beyond this point, with water temps for washing, rinsing, P.H, enzymes, water softening agents, optical brighteners, suds suppressants, ect ect but there still needs to be a sufficient amount of "surfactant" involved in the process, be that SOAP or DETERGENTS. This is why manufactures employe highly trained chemists, to produce something that works in general, and in most all water conditions. But I digress..
If she feels that the Borax kills the dust mites (it probably dose) and is apprehensive about the chemicals in standard synthetic "detergents" then don't forget that she might be O.K with Borax added to some "earth friendly" detergent like unscented Ecos, Seventh Generation ect ect. Most here are not fans of either of these, but I think would agree, they would be better than the online "soap recipe"
( I'm just using them as two example's)
The article you've read on the STPP, I think is a fair one, and I believe is accurate, (even though it's from 2003) Others will weigh in on that, I'm sure!
I know it sounds like we are all trying to steer you away from the "soap formula"... and we are LOL, but, as I said before, if your wife insists, then find out how hard your water is in grains ( your water Dept can tell you ) and send me a email, and I'll do the math including the STPP, and without, in attempt to make it work better than the online formula she using.
HTH