It was Hoster Tully's Castle, who was Bryndon brother (the blackfish). Edmore had three children, all of which preceded the Blackfish in the line of inheritance. Edmore was the last surviving child heir (making the blackfish the next in line). However, Edmore was being held captive by the Frey's, so the blackfish assumed command in his absence.
It's not really minutia as it explained what and why things were unfolding as they did when the Lannisters and Freys were laying siege to riverrun. The blackfish had the right to assume command in Edmore's absence, however, when Edmore was released, he immediately resumed control of the Castle. Jamie had previously threatened that after he released Edmore, if he didn't enter the Castle, resume control, and then surrender, Jamie was going to take his infant child, load him up in a catapult, and splatter him against the castle walls.