DM--
Great clip, thanks for posting.
LBJ had reason, perhaps, for his qualms. After all, LBJ more or less told WC Warren that sidestepping a nuke war with Russia was Job 1.
For you younger readers the idea of a nuke war in 1963 was fresh and real---in 1962, some people thought it was 50/50 the US and Russia would have a nuke war (the CMC).
Here, LBJ seems to be hinting at Russia and Cuba.
BTW---the US Ambassador to Mexico, Thomas Mann, and the State Department staffer in Mexico Charles Thomas, both thought there was a lot to the Cuba-LHO connection, and they were both shut down, and both lost their jobs in short order.