That’s not actually true though. Impeachment is a political process, not a judicial one. An executive can be impeached for whatever the legislature feels like according to rules that the legislature itself sets.
Historically officials have been impeached for such things as drunkenness and “intemperate speeches” (racist rants). If the legislature wanted to, he’d be gone in 30s flat.
Fortunately, it takes due process to “cancel” a holder of public office. Part of that involves verifying claims.