The US Constitution, which outlines many aspects including what the three branches of government are, also outlines disqualifiers for consideration.
You cannot just cherry-pick which few words you like and discard everything else! It's an all-or-nothing thing (as stipulated by the Founding Fathers/signatories and the croonies who've adulterated its intentions/meanings over the years).
When Grand Juries have concluded that an official indictment is warranted, that's more than mere accusations. And "innocent until proven guilty" is not a legal construct; it's simply a moral standard (or verbatim reminder of local judges to their local jurors when considering information in hopes of limiting their prejudice on information demonstrated during trial).