Im an engineering mgr. I hire bunches of engineers and work with hundreds of engineers of varying backgrounds.
I agree with your statement about broad strokes. However, one mans stereotype maybe considered a judicious application of statistics by the initiated engineer
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In general I find many "foreign" workers are talented at analysis and analytical stuff. IN general I find many 'mericans are talented at design and hands on type work.
When I was in grad school my advisor wasnt so PC. She was chinese and said: aschen i dont want anybody but you to touch the expensive equipment, and I want the chinese students to do all the math. I was the only non asian in the small group