The Bloodhound team have read and are following the FIA rules, which I have copied below. What is interesting is that D2.3.3.b still allows interpretation, because it does not refer to whether or not the vehicle is in motion when a device is moved!
Apart from the spelling of movable with an e, which may show that the text could have originally been in French and then translated, Category C vehicles can be aerodynamically controlled, which for supersonic and beyond might be a very good safety factor.
D2.3.3 Category C: Special Automobiles.
D2.3.3.a These Records may be subdivided according to the type of engine used (jet, rocket, etc.).
D2.3.3.b The use of moveable aerodynamic devices is permitted.