“Kellogg’s secret research to make cereal taste better”

“Tesla’s secret battery program”

Neither has negative connotation to me.

Like you said, I think it’s because Facebook regularly acts unethically in public view. Anything they do in secret or private will be viewed with even more suspicion.

I think it's the interplay between both the words, especially considering that Facebook's scandals are privacy related, it might subconsciously trigger some sort of negative reaction when you hear that they are keeping secrets (though that's obviously not what's going on here)