No, sir. US law says all photos taken on or of US military facilities and personel are US property.
On the other hand, the NCO was seriously wrong to order the videos destroyed. Since this was an Army post, the CID should have been notified of their existance. They would have copied them, at least, but more probably confiscated the phone, and taken a statement, to establish chain of evidence.
I was a photographer for the USAF for a decade. Last I checked, the rules on this haven't changed from when I was active duty. There are just more ways of getting personal photos and videos.
What’s the law if you take a photo of a US base or personnel from a public place, not on the base?