Well said. And often, it is a " we would admit you if you had money because you’re clearly the type of student we’d want, but we have no money left" v. rejection (which is not as soft and polite).
It’s absolutely brutal for internationals.
In any case, applying to the same colleges, or to any college that doesn’t offrr automatic scholarships for stats, is pointless. And because many automatic for stats colleges are far below academically what this type of student could attend at home or elsewhere in the world, it’s not worth it and more efficient to go to plan B&C as you said - in this case, a degree from a well-known university, with evidence of solid research, for a funded PHD.