If the price-insensitive people are at home avoiding the crowds then it would seem the online stores would be getting shopped by a higher than average percentage of price-insensitive people.
It appears to me the 'price discrimination' theory doesn't work for explaining sales at online stores.
The essence of the price-discrimination story is not that price-insensitive people avoid crowds. That is more of an add-on.
The basic theory is that occasional discounts are a tool of price discrimination. You keep prices high most of the time to take advantage of people who want it now and are less sensitive to price, and you hold occasional sales where you offer discounts to get business from the people who time their purchases to take advantage of low prices.
This theory predicts that discounts will appear at more or less random times. The question is, why do discounts all get bunched on a certain day? I imagine that once most stores pick a particular day to hold a sale, it behooves you to pick that same day. If everybody knows that Black Friday is a sale day, then nobody will be willing to pay full price on that day, so if you don't hold a sale you will get no business.
The next question is, why is the sale day Black Friday? There is where my story about crowds comes in. If you figure that crowds drive away price-insensitive shoppers, you pick that day for a sale.
But the bunching of sales may be an example of a Schelling point. Nobel Laureate Thomas Schelling said that when people can benefit from co-ordination, they gravitate toward an obvious point. Black Friday may make as much sense as Schelling point for online sales as offline sales, even though crowds are not the issue.