Yes to believing people when they tell or show you who they are. (I actually dated a guy who said up front that he doesn't "do" relationships. I gave him bonus points for being honest upfront, had a handful of really sexy dates? Then moved on to find a guy who DOES do relationships. )
And yes to broadening your horizons to people who might not look on the surface like they meet your requirements. My ex was a highly educated and successful professional. My guy now(Mr Tall Dark and Handsome) lost 20+ years of his life to addiction, suffered all that you might imagine that could entail, smokes (I swore I'd never date a smoker), and although highly intelligent, has only a couple years of college.
And yet, in his sobriety, he is a better man than my ex. Kinder, more loving to me and my family, MUCH more self aware, and so grateful to be free of addiction that he wakes up happy every day. He treats me like a princess and is totally committed to our relationship in ways that my ex never was in 26 years together.