"Psychoanalysis" is a word coined by Freud in 1896, just after the period on that list.
The problem with the fact-check, is that back then, they didn't care much about what was a "symptom" vs a "cause", they called everything an "illness". To be fair, there also was little in the means of therapy; for reference, some "therapies" that were invented afterwards to try to fix that: Incandescent light therapy (1893), Psychoanalysis (1896), Lobotomy (1935), Electroshock (1938). Instead, in the 19th century they used stuff like: moral therapy, hydrotherapy, abstinence, opium... and simply confinement.
"Lunacy" is a very dangerous word when used by a politician towards any group of people.