There’s no “but . . . instead” here. The only piloted reconnaissance aircraft in the entire Turkish Air Force are U.S.-made F-4s (in the RF-4C configuration). And it doesn’t require reasoning to conclude that, because Turkey has explicitly stated that it was a reconnaissance aircraft. Which is fully consistent with Turkey also saying it was an F-4, because, again, all of Turkey’s piloted reconnaissance aircraft are F-4s.
And yes, it is theoretically possible that the plane was doing recon over Syria for the rebels. But it doesn’t make any sense given where the plane was shot down or how both sides say it was flying. If they were really spying on Syria, the logical thing would have been flying high (in order to see as far into Syria as possible), slow (to get more camera time over interesting targets), and along the land border (to peek into Syrian land, where both the opposition forces and the Syrian forces that can hunt them are located). The official radar test explanation makes far more sense than spying on Syria; low-and-fast aircraft are what you want to be able to detect with radar, and over the Mediterranean is where there’s space to run a variety of tests of ranging and locating.
Which leads to the question, why did Syria shoot it? There’s no reason to shoot down a known Turkish/NATO aircraft that was flying over ocean away from Syria unless Syria was deliberately trying to escalate things with Turkey/NATO. But there is no way in the world Syria benefits from escalating things with Turkey/NATO, and they’re pretty openly trying to avoid it now that the plane has been shot down. Why didn’t they do a standard warn-intercept routine?
Well, Syrian radar picked up a plane flying so as to avoid radar headed out of Syria. They didn’t call the aircraft or send up escorts because they didn’t think it was a foreign plane; they shot it down because they thought it was one of theirs. They were trying to avoid the embarrassment of another MiG defection. They didn’t learn it was Turkish until after they shot it down. So now they’re standing on their rights, because it would be embarrassing to admit they shot it down due to an error when trying to save face.
I have stumbled across an article and response written by two brilliant people.