In a management meeting last year, prior to a 15% reduction in force, I brought up that very argument and the likely scenario of discrimination lawsuits. Three months later, the sounds of the cafeteria contained far less Russian and Chinese, and the bathrooms no longer smelled of curry.
Not just the threat of lawsuits from the Americans, but the fact that the law requires you to affirmatively discriminate IN FAVOR of the Americans (that's the only reason the H1-B's are here in the first place). This puts the Americans in quite a strong position. (As it should be, since it's their country.)