Steven Taylor points out that in addition to eliding his own role in the anti-Civil Rights Act filibusters of the 1960s, perennial Signifying Nothing foil Robert Byrd seems to be forgetting that he was Senate Majority Whip (the second most senior leadership position in the Senate, behind only the Majority Leader—the Vice President and president pro tempore are essentially powerless) when the cloture rule on ending filibusters went from two-thirds to three-fifths back in 1975.
Update: Hugh Hewitt, writing for the Weekly Standard, finds Byrd singing a different tune about rules changes in 1979 too (þ: Prof. Bainbridge).