Perhaps the Orcs are like many families and clans that exist today. They will fight, bicker, and backstab amongst themselves, but if threatened by "outsiders", they will immediately band together to defeat them and defend "orckind". So if an outside foe did kill an important member of the band, you probably would find them setting out to seek revenge, no matter what they thought of that Orc personally.
And why not? Orcs were universally reviled. It wasn't like an orc could defect and go over to the other side. Even an orc who claimed he wanted to "sell out" to the enemy would probably never be trusted by the other races.
When you have nothing left, the one thing most anyone will cling to is Pride. And I'd say even the Orcs would agree that Pride is about the only thing they still had going for them.
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