I see a perfectly logical reason for leaving the Treasury – he went to collect the armor. Who knows what else might be in the Treasury, but the armor is right here, close by. While he's collecting it, the looter can check out the underground area. That's a very logical approach.
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You just answered all the questions yourself. Can I ask the same about the Consul... the Consul is here, close by, but he didn't take the last one... and the looter could have scouted the respawn point...