Everybody in the world has fought invaders to protect their land. Nothing special about the sikhs.
You are mistaken about "everybody" joining the british army. Only the designated "Martial race" were allowed. It is something they formed after 1857.That is why you have "sikh" regiment, "gurkha" regiment, "mahar" regiment. etc.
Also find out the percentage of sikhs who has migrated as compared to the population from the rest of India. You will find the truth.
Like I said, the truth is a lot less romantic than the BBC will lead you to believe.