Of course. We have on many occasions, but for "safety" it is always under our control...our cameras/video equipment. No Cell Phones please.
That being said, I can't say that certain public acts haven't been captured by someone that happened to be nearby. I am remembering one time on a completely secluded and private island beach. When we were done and getting dressed to hike back out, we noticed two boats just offshore. Hopefully they didn't record it...that will ruin my chances for public office. 😀