I think Hawkeye wouldn't be boastful in this situation. He was given a responsibility and usually when someone gives him a responsibility he excels at it. Since it's a special responsibility...he will take it seriously. If it was just run of the mill hero work he might get complacent, lazy and arrogant.

Hawkeye wants everyone to respect him. When people show him that respect and make a special point of it he tends to come through.