Sure, lots of pieces of weak evidence can add up to strong evidence... provided they're practically independent from each other. And since this issue gets entangled with Green vs Blue politics, the correlation between the various pieces of weak evidence might not be that small. (If the coin was always flipped by the same person, who always allowed to look which side faced which way before flipping it, they could well have used a method of flipping which systematically favoured a certain side -- E.T. Jaynes's book describes some such methods.)