Convert a QDateTime in UTC to local system time

I construct a QDateTime from a string like this:

QDateTime date = QDateTime::fromString("2010-10-25T10:28:58.570Z", "yyyy-MM-ddTHH:mm:ss.zzzZ");

I know that date is in UTC because that is the way it's stored. But when I want to display this date to the user, it should be in the user's local time zone. date.toLocalTime() looks promising, but it returns the exact same date!

How do I convert date to the system's local time to display to the user?

Here are some more failures:

#include <QtCore/QCoreApplication>
#include <QtCore/QDateTime>
#include <QtCore/QDebug>

int main(int argc, char *argv[])
{
    QCoreApplication a(argc, argv);

    QDateTime date = QDateTime::fromString("2010-10-25T10:28:58.570Z", "yyyy-MM-ddTHH:mm:ss.zzzZ");
    QDateTime local = date.toLocalTime();

    qDebug() << "utc: " << date;
    qDebug() << "local: " << local.toString();
    qDebug() << "hax: " << local.toString(Qt::SystemLocaleLongDate);

    return a.exec();
}

Output:

utc:  QDateTime("Mon Oct 25 10:28:58 2010")
local:  "Mon Oct 25 10:28:58 2010"
hax:  "Monday, October 25, 2010 10:28:58 AM"