Ignoring the flexibility, prices are rigid

I was reading Noah Smith at Bloomberg View:

For example, consider the work of rising stars Emi Nakamura and Jon Steinsson of Columbia University. The dynamic duo of Nakamura and Steinsson set out to investigate the idea that price "stickiness" -- the inability of prices to adjust to changing economic conditions -- is a big factor in causing recessions. The stickier prices are, the more a fall in aggregate demand will damage the economy. Nakamura and Steinsson found that a lot of the non-sticky prices in the economy are concentrated in a few items, such as gasoline, or the result of temporary sales and discounts.

When you account for these price patterns, overall prices in the economy look a lot stickier than economists previously thought.

What does this even mean? Ignoring the flexibility, prices are really rigid? I've written about this before (see here or here), but if a price can do this:

because some executive or the marketing department wants to have a sale, why can't it do that because there is a recession? If I can discount prices by 25-50% on a whim, why can't I discount them for a reason?

Not being able to do that just doesn't make any sense to me. That's why I think prices are micro-flexible, but macro-rigid. But maybe I am misunderstanding something?