This is the nature of rank and position a guy of rank Captain can be in a position of an Admiral and order other Generals and Admirals around in his zone of power, with all due respect of course.
Spectre is a position in the Council space. Council > all. Spectre > all. Shepard could refuse any Hackett's request if it wasn't stupid to act like that.
Also reinstatement of Shepard was a kind of a joke. Shepard joked about not taking orders from Anderson, Anderson reinstated Shepard to be able to give Shepard an order.
There's also this not a Spectre anymore deal. Since Shepard was on trial - her Spectre status was suspended (and then reinstated) - so in fact Shepard was indeed reinstated in Alliance Navy to get going (take the command of Alliance frigate Normandy and her crew). After being reinstated as Spectre, Shepard could literally go to Omega, clean it from Cerberus infestation and dance till the reapers come. Everyone would be pissed, but no one could do a thing about it.