Yes, that is the text of the Imperishable Night, but we can't just look at that. With that kind of argument you could say either Reimu or Marisa could have solved the Scarlet Mist Incident and either of the 3 could have solved the Spring Snow Incident.
But that isn't the case, Reimu is the one who solves both those incidents, as verified by Perfect Momento in Strict Sense.
So, in Imperishable Night, we have 4 possible paths, but only 2 paths are likely. The two being Barrier Team and Scarlet Team.
Barrier Team, because Reimu, by default solves all incidents, unless stated otherwise, like UFO, where it is solved by Marisa B. This incident is also mentioned in Reimu's PMiSS profile.
Scarlet Team, because that team's ending is related to Silent Sinner in Blue.
The other 2 characters could have stopped the night (the how doesn't matter too much), but the scenario is much less likely than either barrier or scarlet team.