Many major Democrats have never accepted the Bush administration as legitimate, not even after he won again in 2004. When Hillary ran many Dims then assumed Hillary had a right to be President. To them “legitimacy” is theirs and theirs alone. When they lose they always claim the only lost because “something is wrong with the system”, and that is when they start trying to change the rules, and most recently the voting rules.
Not only the Bush elections but they never accepted Trump’s win in 2016 Hillary in particular said that Trump knew his presidency was illegitimate.