Perhaps hospitals that treat a disproportionate share of poor people (which themselves are disproportionately not white), tend to use a different brand of X-ray film, and that brand has different contrast ratios than that of the brand preferred by rich hospitals. Thus, they'd be detecting the different brand of X-ray film rather than anything about the patients themselves.

Of course, at this level it's still hard to imagine generating that 82% hit rate. But maybe there are multiple factors along these lines.