Except that—without “nerding out” and getting too down in the weeds—there is a distinction to be made between agents of Parliament and GIC appointees.
GIC appointees act under the minister and under the authorities set out by statute. This means there's a line of accountability in the Westminster system, from the duly elected government down to the appointee, as opposed to agents of Parliament appointed by some summary of Parliament but not actually accountable under the statutory obligations set out in a particular piece of law.
There is a material difference between those two things in terms of how one understands natural justice to have occurred.