It is similar to “off the record”. But generally means the source may be directly quoted, and described (“an Employee”)but not named.
“Deep background” means they should neither be quoted, nor named or roughly identified.
And off the record means they can’t be mentioned and their info or statements can not be used directly.
So basically you’re looking at company spokespeople and official company statements trying to obscure that statements are coming from the company.
Publish our press release word for word, but do not acknowledge that a press release even exists.
