So did the entire 12th (Dutch) Division, which basically stopped existed after Berezina. Not sure what happend EXACTLY at Berazina, but it's possible to advanced and 'charged' on foot. So, I'm not saying at all, that it didn't happen, just saying I find it somewhat odd. The three Dutch infantry regiments had burned their eagle long before Berezina.
That re-enactment group, by the way, doesn't exist anymore. According to same re-enactment veterans 'One moment they were there, in full uniform...and the next moment, they are never seen again".