Why go out and shoot new video when you can find so much off it lying around on the web?
Actually, you probably don't even need to go look on the web. Just look in your own old stock footage. You'll likely find something you shot a while ago that comes close to fitting the bill, especially after a bit of editing.
That said, assuming you do use other peoples' footage, then what you do with it will need to be done modulo their rights.
It's just like sampling. Very short samples of published audio are usually fine, even when that sample is commercially copyrighted (not that I have dared do this myself). Heavily transformed samples are also usually fine, especially when they become more or less unrecognisable.
Recently I needed some ocean footage. Easily found on the web but not obviously free to use. So I eventually found some of my own old stock footage which was OK with a bit of editing (I slowed it down a tad) but the audio was poor. So I took the audio from a web sample and used that instead.
Interestingly, I did nothing to synchronise the waves on visual with the waves on audio. I let the viewer's mind do that for me. I don't think you can see the join.