I am a landlord and use the strategy of keeping rent low but being very picky about tenants. I get lots of "pavement pounders" stopping by when I'm fixing a property up. If someone were to tell me that they had excellent credit, no pets, were not smokers, have no criminal history, and had a stable work history with sufficient income, I would take their information and give them first shot before putting the listing on craigslist. Usually they focus on telling me how much they like the place and that they really want to rent it rather than providing reasons that they are a good risk.
A surprising number of people lie about their financial situation in the initial interview, and so if you're going to provide a credit report, be sure to clarify that you don't expect to get out of the requirement for an official credit report.
If someone comes off as pushy, this is a red flag. So make your case, but don't push for a commitment or keep pestering the landlord.