I don't think that's the case, anymore.
I remember a notorious case, around here, where a guy had a Russian wife (I have no idea of the background -but they were married for many years), he was dying of leukemia, and required her around-the-clock care, and they deported her.
Being married doesn't automatically grant you citizenship. It does give a way to apply for a green card (IIRC, no caps on this path so it's "easy") which then gives a path to citizenship (naturalization).
So; no-duh if the guy's wife is russian she can be deported; she's probably overstayed her visa while caring for the guy.
She was pissed off.
If you just do the paperwork - enter the US under a K1 Visa (fiancé(e) visa), get married, and then apply for a green card once you're married - you won't be randomly deported when your spouse gets leukemia.
It is actually is very easy (multiple people in my family have done this - one guy has even sponsored multiple foreign wives because they keep leaving him cuz he's an asshole). But you do have to do the paperwork if you don't wanna get deported.
I knew a guy that had a Korean wife, legally in the US, but had been, many, many years earlier, swept up in a human trafficking thing.
That made getting citizenship difficult. Twice victimized.
On the scale of least horrible, refugee status might be OK if you can get it, but the anti-refugee climate here has never been worse.