Patriotism can have a hugely different emotional response depending on where you live. It can connote “home!” or “remember, we have weaponized drones hovering above your head”.
Imagine this video feed was from Iran, and ended in a patriotic arabic chant. Would you think, “it is good to see that they are Iranian and proud”?
It is not about being offended. It is about political undertone and tacit military implications.
(That said, I am proud, as a fellow human, of what was accomplished. Also, I live in a country pretty solidly allied with the US.)