BG = bodyguards. Some factions get different, though not allways better, bodyguard units after the March of Time ( Pontos = worth: "ap" sword instead of previous cool mace - less lethality; Armenia = better - armoured Kataphrakts; etc. ).
If you want to grant a faction a settlement you should offer them some money, say 2k mnai, otherwise they´d reject... You could also install "Forced diplomacy" mod, then AI will most likely accept any treaty which is not contradicting with their vital interests, or is impossible for them to fulfill.