Seems like this depends on what you mean by "large group." If we're only talking about, say, populations of entire large countries, or all adherents to a major

Seems like this depends on what you mean by "large group." If we're only talking about, say, populations of entire large countries, or all adherents to a major world religion, then sure, it would be very unlikely to get them to literally all agree that some error was made. But that's mostly because it would be difficult to coordinate any behavior that specific across that large of a group of people. If, however, we're just talking about the official leadership or representatives of some large group, then there are plenty of cases of them admitting mistakes. Even big companies and governments occasionally admit mistakes.