There seems to be quite a bit of literature that flatly disagrees with this statement. Perhaps you could add a source? The conventional wisdom where I'm from is that multilane roundabouts don't reduce the absolute number of crashes (and might even increase crash rates), but they still dramatically reduce the severity of crashes.
Canada:
> However recent data in the United States and Canada are showing that collision frequency at multi-lane roundabouts is often higher than expected, and sometimes higher than the prior signalized intersection. This trend is worrisome given that roundabouts are often constructed as a means of increasing safety. The good news is that fatal and injury crashes are almost always reduced with roundabouts, even if property-damage-only crashes are not.
https://www.tac-atc.ca/sites/default/files/conf_papers/weber...
Netherlands:
> Multi-lane roundabouts. These are less safe than single-lane roundabouts, but still safer than other types of intersection [22]. Multi-lane roundabouts are less safe because they have a larger number of conflict points, they are more complex, driving speed is higher, and they have a less sharp entry angle [23].
https://swov.nl/en/fact/roundabouts-how-safe-are-different-k...
US:
> Roundabouts force drivers to slow down and all but eliminate the most severe types of intersection crashes — right-angle, left-turn and head-on collisions. Single-lane roundabouts see fewer total crashes of any type.
https://www.iihs.org/news/detail/safety-at-two-lane-roundabo...