It's about uncertainty though so it doesn't really work if you know it will turn up (also 1 minute is hardly a delay).
People would probably choose a system of 0-30mins delay with no info vs 0-60mins with info, if they know thats the rules. 'it'll be here within half an hour' is close enough to knowledge to get the uncertainty out the way which is a lot of the problem.
But if passengers don't know what the rules are or when (or if) the train is coming, and you'll get a lot less complaints and grumbling passengers with a 0-60 full info delay system then you do with a 0-20 with no info. In one you know the train is coming in 47mins. Annoying, but you can tune out for 30 mins, get a coffee, read hacker news, tell a friend you'll be 47 mins late etc. In the other it might be here in 2 mins or 20. You can't even nip to the loo without concern you might miss it. In the first instance you are mildly annoyed but you replan your time; in the second you're on edge for what turns out to only be 8mins, but a highly annoying and stressful 8 mins.
It's the uncertainty that's painful not so much the delay (for small-ish values of delay!)