It's "a sleazy Indian (operated) casino" vs. "sleazy American (cuisine) diner".
The first is referencing the ethnicity of the casino's operators, the second is referencing the style of the diner and doesn't infer anything about the ethnicity of the owners.
I see the sibling says "Indian" could be considered wrong.
However, again, with you post why is it wrong to say their ethnicity? Incidentally I was plugging for American as being an indicator of ethnicity; there's also a subset issue so for "sleazy American diner" read "sleazy Greek bar" (a bar in Greece, though it could be a bar run by a Greek I guess it doesn't seem to matter).
The first is referencing the ethnicity of the casino's operators, the second is referencing the style of the diner and doesn't infer anything about the ethnicity of the owners.