So don't assume that what applies to humanities applies to every research field.
As you may or may not know, on Nature Communications (and on many other journals of Nature Publishing Group) you can only publish open-access, so that's effectively a fee you have to pay to publish on Nature Communications.
You pay, you get your paper published. You don't pay it, your paper is not published.
As you see, your definition of grey literature includes one of the most prestigious journals in the physical sciences. Time to revise it! Better late than never!
> Don't come to my university.
If I do I hope that at least your colleagues will be able to see beyond their nose, and will know that what's standard in humanities may not be standard in other fields.
> Open access fees are very expensive everywhere.
Which is exactly my point. The EU announces that all papers will be free to read, so open access? Someone must pay. The price will be paid by research groups, smaller ones may not be able to sustain it.
The publication fee for Nature you mention is for open access, not for publishing. Open access fees are very expensive everywhere.
And no, my definition of grey literature is completely fine. Don't come to my university.