By "guaranteed minimums" I was referring to A-basis. There are manufacturers who use terminology which sounds like that in their promotional literature, problem being they rarely specify where it came from.
S-basis and the like (Matweb, Metals Handbook, metallurgy textbooks) are only good for low risk/low hazard applications, or as a forecast until a proper test program can be run.
Yes, specific lot testing would be required to use "premium selection" on a continuous basis. Many companies have internal specs which already do this. Most modern quality systems require mill certifications anyway; so the actual mechanical properties (and chemistry) of that batch of metal are at hand (not sure how you'd handle this for an overload, unless it's the mfr). The trick is to make sure the test methods are consistent, and they usually are.
Another way to look at it is the mill certification is a sample size of one, part of many data points that long ago went into the number cruncher to come up with MMPDS A- and B-basis values. Your only uncertainty is the calibration of the mill's lab, and that is a minor concern.
I do lots of one-offs and rapid jobs, and actual material properties have saved the day. For instance, I have seen a mill cert of 7075 with Ftu of 109 ksi AND elongation of 12%; coulda swore it was steel. It helped out when there was a small negative margin (in comparison to MIL-HDBK-5), after repair was in place. With the actual lot strengths in hand, voila, problem solved with a change order to specify a minimum strength.