There is a Hebrew expression explained here:
A common Hebrew expression is "Respect them and suspect them". We should always act in a respectful way towards others, but that doesn't obligate us to trust them with our property. The source of this is in a story of the Talmudic sage Rabbi Yehoshua. A complete stranger asked to stay the night. Rabbi Yehoshua obliged him by giving him a room in the attic, but also exercised prudence by removing the ladder so that the guest wouldn't be able to sneak out. The guest turned out in fact to be a thief; he wrapped all the valuables in the top floor in a cloak and tried to sneak out, but fell in the dark because of the missing ladder, and was caught red-handed. (http://www.aish.com/ci/be/48918612.html)
Do we have an expression in English to this effect?