I guess it may be different from car to car but my fuel cut always happened when I strayed over 1.0 bar for a few seconds. It's when the ECU sees a certain voltage from the MAP sensor, so if it's slightly out then you'll get fuel cut at a slightly different point.
You're correct about the fuel pump and gauges not being *required* for BPU, but it's all about mitigating the risk. You ran 1.2 bar, and said all was fine, but who's to say you weren't running dangerously lean and if you'd kept going another few seconds you could have damaged the engine?
Perhaps someone more knowledgeable will correct me if I'm talking crap, but I think that's the main reason most people do BPU in a certain way.
Also - the best FCD (Thor/TRL, secondhand £40) allows you to set the new fuel cut threshold at another level, say 1.3 bar so if something does go wrong you'll still get fuel cut.