I remember a line in the move where one character was called either a bastard or a son of a bitch to which he replied similarly to your line, "Mine is an accident of birth but you, sir, are a self-made man".

As for where you draw the line, Wikipedia, for what it's worth, draws two lines. One is 1912 based on the last few territories becoming states. The second line is 1924 based on what the writer calls the "myth of the Old West".

Personally, I always considered "The Professionals" to be pretty close to a western.