Let me please add my voice to the few have said this is complete and utter bull crap.
Integrity does not have a proximity setting, it does not bound itself by space or time, nor scenario. Situational integrity is an utter fantasy as well. "I had to in this case ... ." Bull crap. It was convenient.
Having integrity can be hard. Doing the right thing no matter what is a grueling exercise that at some point in ones life is bound to fail ... and that's okay ... because its how we learn. I've learned a bunch and am sure I will continue to.
J.C. Watts famously said, "Character is doing the right thing when nobody's looking. There are too many people who think that the only thing that's right is to get by, and the only thing that's wrong is to get caught."
Look at the state of sport today ... not just the NFL, although that league is a particularly (bad) example (look here for the USA Today arrest database). Players, coaches, management, owners, referees all ... what a mess. You have HOF players giving advice to basically get a "fall guy" for the screw ups you are going to have.
Here's a novel idea ... DO THE RIGHT THING.
Yes, it's hard sometimes.
Yes, it's inconvenient sometimes.
Yes, you may lose out sometimes.
But, you will be better for it.
Now, some may say, well that's great Mr. Goodie Two Shoes, but everyone screws up.
Yes, I agree, and am in the front of the line in that department. In such a case you have to own it. Fully. Completely. Unconditionally. You also have to sincerely apologies for he screw up, not this "I'm sorry if I offended anyone" crap.
Anyone remember Jim Joyce? Here is a reminder, with his response to a screw up from him:
If you ever need an example of owning it and doing the right thing, here it is.
Integrity of the game is a myth ... it is the integrity of the individuals that are involved in the game that counts.
My #protip in this area is BEFORE you give a player a second caution, CHECK TWICE. To accidentally give a player a second caution when they did not earn it has tragic results. I know, because I have done it before. Check before you do, and if you screwed it up, take it back right there. Don't punish a player for something they did not do. Own it. Apologize. Move on.
You will earn the respect of all involved and maintain your integrity in the process.