It’s a pass/fail, but I have personally seen no one fail during my own trips, and I’ve seen a lot of things in this regard — including US airlines’ security contractors demanding illegal things such as the presentation of non-existent illegal ID to fail the traveler/travel party.

The extra screening of this sort is generally way less likely and/or less serious when flying non-US carriers to the US, even when flying from the very same European airports to the US.

BA from LHR to the US tends to have substantially less of this kind of thing going on at LHR than AA, DL or UA. While several European carriers to the US do now have SSSS flagging going on and additional screening going on as a result of that, it’s generally not like what goes on when flying US carriers from the EU. For example, LH group airlines have sometimes hit members of my travel party with SSSS, but each and every one of those circumstances was less intensive than what you described and has often been waived for me, something the contractors working US flights for US carriers have never done for me.