I'm sure the facts will present themselves over time. The statement out of United appears to me to be a PA-friendly statement that chalks the incident off to an accident and doesn't accuse either party of lying about what happened while they try to find a way to placate the offended passenger off-line and not incur the Congresswoman's wrath. I'd probably try that route myself if I were in United's shoes because they're in a no-win situation.
The problem with UA's story is that they boarded the passenger in question. If she had cancelled (via app or otherwise), she wouldn't have had a valid boarding pass for the flight, period, end of story. I have no doubt the press would expose this logical fallacy for what it is if this was someone they despised but they will do their best to bury it for someone they like/prefer.