Why is MP4 black background gray in Internet Explorer 11?
The solution was to turn off IE-11's "hardware acceleration" feature which (says here) "lets Internet Explorer move all graphics and text rendering from the CPU to the Graphics Processing Unit (GPU)".

I disabled that under Tools -> Internet Options-> Advanced by selecting "Use software rendering instead of GPU rendering".  It's pictured here

Then, after obligatory re-start (of IE), all the grays were black and colors bright in IE-11. 
Now, how I communicate this knowledge to IE users viewing my washed-out videos is a tough new question.