It was stated that the bad thing damages the room and the people in it as well; I took this to mean physical damage possibly leading to death because otherwise it doesn't make any sense. Therefore, with the two options that we are apparently forced into, the group is doomed regardless. It's only a matter of time. I say forced into two options because of the artificial restriction that the people cannot leave the room, which was not stated in the original explanation. Another out would be for the group to kill the visionary once he started back to doing the bad thing, remember that this damages them, which showed he could not be trusted and did not care for the well-being of the other people in the room. Is that not an option as well? In the end, the only choice the people had to fit their best interests was to leave the room, unless you can justify the murder of the visionary. But you took that away and I'm led to believe that they have no other options, so in the end they are all doomed regardless of either choice they go with.
Changing the rules, or adding new rules as I respond, to change the thought experiment is not a good way to invalidate my conclusion. For instance, equating a room with the Earth doesn't work for me, that's different situations with different potential outcomes with different options. The bad thing in a room thought experiment, as presented, is simply a bad example if there are only two options allowed.
Now, if we're talking about a situation you are describing, where the outcome is not damaging to the people involved, except for maybe their sanity, then I can somewhat agree with what you're saying.