For the first time in 15 years a D'addario string was defective, it couldn't be intonated. The 12th fret harmonic and the open string had the right pitch, A, but the fretted note at the 12th was an enormous 15% low. Shortening the string with the intonation screw changed nothing, the fretted note at the 12th and surrounding notes were much too low.
Notes closer to the nut were good but past the E note their intonation was more and more off. The saddles were staggered as they always are, I have several electrics so I can eyeball that and be very close to the right intonation. I thought maybe the top part of the string is thicker, but no, it's 0.78mm to 0.80mm wide all along. The coil has no irregularities so I had the crazy idea of unwinding it to see the core but that would be a mess, and maybe useless, the defect might not be visible. Could be a tempering problem.
So, why the string sounded awful is still a mystery but the replacement sounded right immediately, the saddle's position in height and length was good. Only a half-turn of the length screw was needed to perfect the intonation. Now I just have to play that string alone for a few hours because the others have already lost their fresh string tone, the new one's brighter sound makes it stand out.
After streching it properly the string keeps its pitch for a long time with very little retuning. Problem solved.
I have to say even the so-so stock strings made of recycled barb wire on my unexpensive guitars never had that issue, so the string making industry as a whole is very reliable. But the D'Addario tone is something else.