On Federal property, not public and/or private . . .
The bought-n-paid for American Flag remains personal property, to be used/displayed as one wishes. The rules you infer should be observed when on Federal property, such as a national parkland, but remain difficult to enforce even there, as many are now so ignorant of these rules. Used to be taught in school, the Boy Scouts/Girl Scouts of America, even in local children's recreation halls -- a facility I have not seen for decades.
Bringing up the issue of improper Flag display at a KOA for the edification of an offender, though, is a great way to make them feel, at the least, self-conscious. Later on, they may even get a bit o' readin' in 'em.