Doing the math, it is extremely unlikely for a lot of coin flips to skew from the weight of the coin.

To that end, observing unanimous behavior may imply some bias.

Here, it could be people fearing being a part of the minority. The minority are trivially identifiable, since the majority signed their names on a document.

I agree in your stance that a majority of the workforce disagreed with the way things were handled, but that proportion is likely a subset of the proportion who signed their names on the document, for the reasons stated above.