To my mind that's logical. A BA issued boarding pass is drawing on its own data and Amadeus. An AA issued boarding pass does likewise only their GDS is SABRE.So BA tell you what they know (even if for a UK depart it's incorrect, the relevance is of course for the return to the UK), and AA have their own ownership of Pre-Check, based on a separate arrangement they have with the TSA. The fact you have Pre-check on your subsequent flight is all due to AA, not BA. I know one could mutter about seemless travel, but over in the real world.....