To any one who reads this, don't actually do that. I wouldn't put it past Facebook to file a serious lawsuit against you. If it spread far enough, you could cause serious damage, and the SEC might even get involved.
If I were going to do this, and I thought it would cause such a storm, I'd take a raspi wardriving and find an open router somewhere, and then upload it via TOR to liveleak or imgur or something like that using an old netbook sourced from Craigslist. Then wipe the devices used and sell 'em back on Craigslist, or drop 'em off at Goodwill or some recycling company. Plausibly deniable and all that.
Some one's been watching too much Mr. Robot... for what it's worth, don't bother with imgur over tor; they block uploads from those ips. You can, however, use the lunapic upload to imgur feature. Public library also might be an option, though I might reccomend i2p. Whether it's really "more secure", I dont know, but it doesn't have the same mainstream knowledge (or use by journalists), so three-letter guys would be slower to break it.
"Speaker Nancy Pelosi on Wednesday strongly rebuked Facebook, saying the company’s refusal to take down altered videos of her demonstrated how the social network contributed to misinformation"