Lots of bhind the scenes intel information in this post may help with background details during that period of time - in relation to Burgdahl.
According to this UKGuardian Jan,2012 account, early negotiations for the GITMO-5 did not mention Bergdahl as part of the bargain:
US agrees in principle to releasing top officials from Afghanistan insurgent group in exchange for starting process of negotiations.
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Keep in mind, this took place while Hillary was SoS
(Administration Mum on Talibans Call for Release of Guantanamo Detainees - January 4, 2012)