Quote:[As the old
cowboy saying goes: "The hat is the last thing you take off and the first thing that is noticed."]
(see for fine performance of this saying : Clint Eastwood)

In contrast to the Dutch proverb:" With your hat in your hand you'll get through the entire land."
(meaning politeness gets you a long way)

Could this be considered as s a case of proverbial contradiction?

Headaches:
A crown's no cure for a headache.
Every head has its own headache.