Most people use a narrow definition of integrity. Joe Typical figures that, so long as he never tells an outright lie, then he has preserved his integrity. Innocent until proven guilty. This works fine if your only concern is how you appear to other people. It permits a variety of deceitful behaviors, such as allowing another person to continue in a mistaken belief, or failing to tell someone something that they should know.
Most people engage in such behaviors.
The reasoning used to justify such behavior is destructive to clear thinking. It is impossible to engage in deceptive behavior without in some way believing the untruth in some corner of your mind. To say it, you must first conceive it, and to conceive it, you must erect the mental construction somewhere in your mind. You must build a little wall to seal off the falsehood. Every time you tell or even think anything less than the absolute truth, you create a little wall in your mind, and then you must maintain that wall for as long as the consequences of the falsehood might come back to you.