what's this "Ugly American" business? Are Americans considered ugly in Poland?
The business actually comes from a book called "The Ugly American," a novel based on history of America's failures to win the hearts and minds of people in SE Asia during the Vietnam War years. It has become the idiomatic way of pejoratively referring to Americans abroad, because the stereotype is that they are fat, loud, and rude - in a word, ugly. No, not everyone in America is ugly, but not everyone looks like they do in hollywood movies either (slim, tan, muscular, fit, sexy, clear skin, etc).
To the OP, wear your fanny bag if you must, after all we can't teach an old dog new tricks. Just be aware that they are popular targets for pickpockets because they scream "clueless tourist" to the local thieves and suggests that there are passports and moneys inside...