The organisation, which serves as an umbrella body of Muslim groups, showed a 57-second-long clipping featuring two personnel of the Sashastra Seema Bal talk about Shah and how he entered India with his family.
"Some days ago, some people had come through the border. Routine checks keep going on. When we questioned them and saw their documents, we had some doubt because the documents they had did not look valid. So, we thought we should question them properly," one of the SSB personnel was heard saying in the video clip.
"Later, we got to know from the news channels and media that the man, Liyaqat Ali Shah, whom we had detained and handed over to security forces has links with Hizbul Mujahideen."
Asserting that the video "discredited" all claims by Special Cell that Shah was arrested from a railway station in Gorakhpur, the panelists said that the cell had "put in danger a very important government scheme to end militancy in Kashmir".
Responding to the allegations, a police official in Special Cell said, "Why should we be against the rehabilitation policy for militants? We have always said that Shah came through the Nepal route but he was arrested by our policemen from Gorakhpur railway station."
"As for claims by 'SSB officials', I cannot comment on something that I have not seen. The credentials of this video are to be verified," the officer said.
Meanwhile, the special NIA court on Tuesday granted permission to the National Investigation Agency to interrogate Shah in judicial custody.