The phrase "actually document" is correct and usable in written English.
It can be used when referring to the act of formally recording or providing evidence of something.
Example: "We need to actually document the changes made to the project for future reference."
Alternatives: "formally record" or "officially note".
For example, they didn't realize that you can't just start writing out checks, you have to actually document needs.
When I pointed out to Druids that they could not actually document their descent from the Grooved Ware people, the conversation often took an emotional turn.
Lavish amounts of well-informed speculation, applied like plaster, hold together the bits she can actually document, but the result is a narrative that could have come straight from Trollope.
Clark McPhail, an emeritus professor of sociology at the University of Illinois at Urbana-Champaign, and one of the first people to actually document and study how people behave when they come together in large gatherings, doesn't even like to use the word "crowd".
Take Sacramento, which for years has rebelled against installing water meters, which might actually document how much water residents and farmers use.
And so that meant we had to figure out how do we actually document, and accept, and verify memes from other cultures.
There were rumours of giant squid in the ocean for a long time before scientists actually documented one.
It's not just that they were what one would call an open secret; the pacts were actually documented in papers the U.S. government declassified years ago.
But they are inherently pseudo-scientific — because if they weren't, and were actually documented and studied by scientists, and actually existed, they'd cease to be as compelling.
Banners also figure in a video by Traci Tullius titled "Unflag (of UnParade)." Although the film seems to record placard-carrying, flag-waving marchers in a political demonstration, it actually documents a Lower Manhattan arts festival.
Playing on a small monitor is a smoky black-and-white video that could easily be 30 years old but actually documents a performance on the stage at the show's opening.
