1. A term frequently used by politicians when accused of something scandalous. It means: "I did it, but as long as there's no smoking gun I will deny it completely." Most such scandals involve illicit sex, bribery, influence peddling or misuse of public funds.
2. A worn-out public relations phrase that nobody believes anymore. Nixon's famous remark -- "I am not a crook" -- sounds positively Shakespearian in comparison.
"The accusation is categorically false!," said South Carolina Republican Nikki Haley. She is accused of having an "inappropriate physical relationship" with the governor's former press secretary.
For such a thing to exist, there must also exist its inseparable opposite. It's, very clearly, a non admission admission, that's synonymous with "compartmentalization", which is where we must look for an in depth understanding of its true meaning.
No clear examples of categorically false may be given without criminal implication, since it is only they who use it.