If it's Anne McCaffrey it is probably in Get Off the Unicorn, cause I only have so many books with her short stories in.

Web searches suggest it is Dull Drums?
I should go find it on the shelf and check...
yes, found it! Dull Drums it is!

... but I dont think I summarised it accurately. Re reading a bit of it, it was about people starting to trust computers, specifically that private data would stay private. Huh. Not same thing.

ah well.