Keep in mind that this was pre-Twenty-Fifth Amendment, when matters were less clear. There was a debate in some circles whether the Constitution intended for the veep to become President or acting President. John Tyler’s precedent (objected to by the usual suspects of his day) nominally settled the question for the former, but it was still open to debate.
In any case, the VPs who had previously succeded to the presidency all insisted in taking the oath ASAP. Given the circumstances and LBJ’s own insecurity in the situation, taking the oath was important for symbolic reasons, if nothing else (after taking the oath, no one could argue that he technically was not President).
It wasn’t until the Nuclear Age that we had to worry about the Vice President having full presidential authority the moment the President died.