As for your problem with the first trial, are you sure you just weren't pressing the button right? If I remember correctly, that's one of those "Hold the buttons" sequences, so if you kept just hitting the button it wouldn't work.
Yup, I'm pretty sure it was a bug and not my problem. Although it was a tense moment, there was enough time to experiment and retry quite a few times, and by then I was familiar with the controls and on-screen prompting; nothing worked, there was not even the usual on-screen feedback. Given that similar things happened others times where was incredibly obvious it was a bug (e.g., in the train station, where the
movement controls completely failed to work -- until I restarted, whereupon they worked normally), it seems reasonably clear that the game is just buggy.
Note that my PS3 is not online, so Heavy Rain was running completely unpatched.