Reason one is actually disputable as a reason not to notify. The cop saw his card, he never offered it, and it went from there.
If you're going to not inform, letting them glimpse the card is an instant inference that 'there's a gun and he doesn't want me to know'.
That's going to immediately throw an alarm, c'mon.
I can't see the video for number 2, but I don't doubt there are overreactions. Suggesting potential overreaction is a reason to not inform is almost as good as suggesting mass shootings is a reason to ban guns. Different subject matter, same logic. Same as we can't prove the number of mass shootings stopped by carriers, how many no incident voluntary informs happen is immeasurable.
It amazes me we, as gun owners/enthusiasts/whatever, quibble over things like this, then wonder why we keep losing rights to slow paced erosions. Each of us has experiences that influence how we interact with LEOs, or anyone for that matter, and should understand that we're all different and going to approach things somewhat differently.
As an insight on situations like these, I will share my personal line of reasoning - don't apply the following to yourself and get all boohoo if you disagree, this is my opinion.
There are expectations required of oneself if you are going to carry a firearm.
-You should be proficient in the safe handling and operation of it.
-You should never break the 4 rules
-You should be prepared to use it if necessitated
-You should know what situations define necessitated to you
-You should be prepared to wind up face down on the ground over it
-You should be prepared for the ensuing legal nightmare that may arise from using it
If I couldn't make it through this list I would not carry. I'm sure some will pick apart these 6 points (especially 3-6), but this is what I feel necessary to justify carrying.