Funny thing.
Every ER nurse/doctor I've ever talked to or read posts by has said that they can tell when "I fell down the stairs" is a lie. Car crashes are 10% of all injury-related ER visits. I can't find statistics by intent but non-firearm assault is something like 5% of injury-related ER visits. They do this every day, they've seen everything you can imagine and more, and it is literally their job to figure out what happened. They are very, very good at it.
Car accidents leave distinctive injuries. So do beatings. For example, there's nothing in a car accident that'd leave knuckle-shaped bruises. Nor is there anything that'd pull an arm straight off without massive other crushing, tearing, and piercing damage to the hand and wrist, all of which would be decidedly absent given the way Red Skull pulled Liv's arm off after taking a solid grip on it. A car crash wouldn't leave distinctive bruises and split skin on Liv's knuckles. Airbags leave other unique injuries that Liv doesn't have. And that's not even getting into how Liv's armor and arm-harness would have changed how she bruised underneath them.
In other words, as far as I know, it should be blatantly obvious that Liv didn't lose her arm in a car crash. In fact, I wouldn't be surprised if the ER professionals can get all the way into the specifics, figure out that she was injured in an implausibly high-intensity fistfight between people with body armor that culminated in Liv's assailant ripping her arm off.
I don't know if that's an intentional OOC complexity to Liv's visit or if it's just not something the author knows about. I'm leaning toward it being unintentional, mostly because it doesn't seem to offer any new explanations when I look at what happened in this update. But it's certainly a way for Cap to track Liv down if he wants to, isn't it?