Did I answer in the wrong way??

I was recentely being pursued for a wonderful job and came back with excellent recommendations from referances and emplyment history. On the application it asked if I have ever plead guilty or been convicted...., back 20 years ago I had a conditional discharge that was successfully complied with and dismissed. So according to state I never plead guilt or have record of conviction, only an arrest. Arrest was not mentioned on the application, so I put no since I was not "convicted". When background check came back they had a hit, which I explained in detail to them and even sent them all info regarding event. Well the next day they called me and said the job would no longer be offered to me because I answered no on application. I guess they thought I lied, even though I had nothing to hide, and told her such. I am now going to pay thousands of dollars to expunge this mess which cost me my dream job. I guess I wanted to inform everyone out there with a very old past to be wary of how applications are filled out. I feel that I was done wrong, and it is humiliating to say the least. Thanks for listening, now to go back and hunt for jobs!