As we've seen on numerous occasions throughout Star Trek
, Spock appears to have an understanding of temporal mechanics that is superior to most of his colleagues. It was Spock who implemented the "slingshot" maneuver used in "Tomorrow is Yesterday," "Assignment: Earth," and The Voyager Home
. It was also Spock who correctly deduced that the Guardian of Forever could be used for time travel, as well as determining that time's currents would likely sweep McCoy to the same time and place that he and Kirk had been drawn to in "The City on the Edge of Forever."
We've seen autonomous departments within the Federation recruit experienced officers before, such as when Section 31 added Dr. Bashir to their ranks, albeit against his wishes. The following question must therefore be asked: would the DTI have any interest in recruiting Spock? Or, perhaps a better question might be, has Spock already worked for them, thus explaining his proficiency in temporal mechanics in the first place?
Section 31 prides itself on covering its tracks, but the DTI can completely erase their tracks from existence if they so desire. Who's to say that Spock hasn't undertaken missions for the DTI? What might the consequences of those missions have been?