I have a degree, clean history, heavy, international PIC experience, recommendations, management and training experience, etc. FedEx turned me down. For better or worse that was their call to make. Them's the breaks. I say this so you know that my response will most likely NOT affect my chances with FedEx.
If you're thinking about walking away from your job, by all means get the heck out of FedEx. Mistakes happen, and you're in the wrong position. Although FedEx certainly has dirty laundry, you're leaving the happiest pilot group in aviation. So be prepared to find the same malaise at your next job. Do your research next time and be honest with yourself about who you are. Perhaps aviation isn't for you?