I suppose you can trust them to lie! :-)
The real question is: Why would anyone want to invest their time and emotion in a relationship that lacks honesty? There are 7 billion people on the planet! Surly one could do better than that.
In my opinion "trust" like "respect" are to be given overtime. A person has to demonstrate honesty and integrity before I would trust them with something as important as my heart. Having said that everyone is entitled to have their own "deal breakers".