If the Landlord took his time to make sure that he had the right tenant in his property, yes will be fair to dismiss any first time ofense. It really depend of how bad is it? Remember normally people keep repeating their mistakes over and over.
Renting is a business. It is hard and harsh when one mistake is preventing you from moving forward. But what is fair is really up to the landlord and if there are other applications that are better, the landlord has to make a business decision. If you want to be given a chance to prove yourself, you will have to make your application look better or offer the landlord more security or more to give them an incentive to give you a chance. Good luck.