It's possible the Enterprise
crew were under Talosian influence before they got to starbase. Kirk says Spock received a message from the starbase---but why Spock and not whoever was manning communications? Even if it was a personal message intended specifically for Spock it still comes through the comm board.
Given this it appears the Talosians were manipulating pretty much everything. There could even have been an illusionary Kirk back on starbase fooling Mendez long enough for the real Kirk (with illusionary Mendez in tow) to attempt chase in the shuttlecraft.
The attempted chase in the shuttlecraft makes little sense either. Even a warp powered shuttlecraft would have no hope of catching the Enterpriise
if the starship really steps on the gas. The starship would have to be pretty much puttering along at maybe Warp 2 or 3 or so and staying teasingly just out of the shuttlecraft's reach. If the plan had been simply to grab Pike and go for Talos 4 then the chase would have been thoroughly pointless. Obviously everything was staged so that in the end Spock is most likely to be exonerated.