Ya it seems that you should have a mandatory amount of "allies" if thats the direction you're going to go. Eldar admech and SM seems the most likely to stand out due to their already above average leadership. Im going to have to take a look at this on the computer to get a better view because a few of these seem pretty off (Admech trusts Tau more then IN or space marines?)
Ok so looking at these this is where I would think they would fall.
Admech allies: Chaos orange, Inquisition yellow, IN green, Necrons orange, Space Marines green
Chaos allies: Admech orange, Inquisition yellow, and Space Marines red
D Eldar allies: DE green, Eldar green, and Inquisition orange
Eldar allies: (includes CWE?) DE green, and Inquisition orange
Inquisition allies: Everything should be yellow or orange, except the Nids
IN allies: Necrons orange
Necron allies: Admech orange and Inquisition orange.
Ork allies: Rogue trader yellow, SM red
Rogue trader: Inquisition SM and orks yellow.
SM allies: Admech green, Inquisition yellow, orks red, Rogue trader yellow
Tau: Inquisition orange
Nids: red lots of red and more red.
Ordo Hereticus Inquisitior Lord allows for Admech, Inquisition, IN, RT and Space Marines as Green allies.
Ordo Xenos Inquisitior Lord allows for any one alien race to be yellow. *except nids
Ordo Malleus Inquisitior Lord allows for Chaos as green allies.