Allied Detachment rules:
This Detachment cannot be your Primary Detachment.
Your Warlord can never be chosen from this Detachment.
All units chosen must have the same Faction (or no Faction).
All units chosen must have a different Faction to any of the units in your Primary Detachment (or no Faction)
The reason why the chart shows that you are Battle Brothers with yourself on the matrix is because of how abilities affect your own stuff, but also when you have things like Crimson Slaughter, Black Legion, Chaos Space Marines all class as CSM for the allies matrix. However you are not considered to be the same faction.