The word "integrity" has a positive connotation, but it doesn't simply mean "goodness". It also means consistency. In that sense, it makes sense to call the way

The word "integrity" has a positive connotation, but it doesn't simply mean "goodness". It also means consistency. In that sense, it makes sense to call the way we act differently in front of different audiences a "lack of integrity". So, I agree the statement is a bit robotic (specifically because it points out a natural part of human behavior as a character flaw), but not that it's twisted.