Check out 16 minutes in on this video (also check out the Kevin Bacon lookalike right after that clip at 16 minutes):
I think Ramsey Clark was confused as to who the FBI interviewed after the assassination. To my knowledge, Shaw wasn't interviewed/questioned at that time. The FBI did receive a claim shortly after the assassination about a "Clay Bertrand" calling a New Orleans lawyer, Dean Andrews, on the even of the assassination asking if he, Andrews, would represent Oswald. And the FBI then searched for a Clay Bertrand in New Orleans and couldn't find one. But they did nothing at that time involving Shaw.
So my hunch is that Clark mixed up Bertrand with Shaw.
Max Holland mentions this error here:
https://www.theatlantic.com/magazine/archive/2004/06/the-assassination-tapes/302964/He writes: "Although the FBI had examined an allegation involving Ferrie, it had never investigated Clay Shaw in connection with the assassination. Johnson was probably just repeating what Ramsey Clark had said earlier in the day. In response to questions from the media, Clark erroneously asserted that Shaw had been investigated by the FBI in 1963, and cleared. Clark's error would not be acknowledged for three months."
BTW, the Holland book on the tapes is really fascinating. It reveals that behind the scenes LBJ and his people, e.g., Clark, were confused and puzzled at what Garrison was doing and about matters related to the assassination. We think that the President and other top officials are always given accurate information and are on top of things; but they're not. But conspiracists will say - again - that this was all an act. LBJ was pretending not to know.
FYI, I edited out your link to the tape/video.