It says in the Gemara that we can say Shma until the third hour since that's when kings get up.
What kings are we talking about? Jewish kings weren't around until much later, so Sof Zman Krias Shema couldn't be based on their behavior.
On the other hand, would we establish "zman kima" (rising time) from non-Jews?
(Moreover, one can infer from Tosfos that "Zman Kima" is Jewish "Zman Kima" from his question on daf 2b where he asks on the opinion that the time to say Shema at night is from when a poor person eats his bread until after he gets up from his meal, that when does the poor person say Shma? If one counts a non-Jew's times, one can answer that the "poor person" mentioned in the mishna is a non-Jew, and a Jewish poor person eats at a different time.)