I know what my father told me. I believe him - I have never known him lie.
The swearing-in was not filmed, so the only way your father could have seen the look in LBJ's eyes at his swearing-in is if he was one of the following people:
JFK's Press Secretary Mac Kilduff
Former MPAA President Jack Valenti
Congressman Al Thomas
Congressman Homer Thornberry
Congressman Jack Brooks
Bill Moyers
Secret Service Agent Roy Kellerman
Secret Service Agent Lemuel Johns
Dallas Police Chief Jesse Curry
White House photographer Cecil Stoughton.
If one of those guys is your dad, the credibility of this story improves dramatically.