When entering the military, if you have any issues (either medical or judicial) you must submit for a waiver.
The waiver process is considered an appeal for entry, however, it is based upon a person's opinion and you are not allowed to appeal their decision, it's final. Although, you are told that you are more than welcome to contact your congressman, who does not have the time to fully investigate the claim and support you.
If you are allowed to appeal, you would be able to submit amplifying information to be reconsidered for the waiver.
This would allow people who wish to serve in the military the chance to actually do so, especially people who don't have a disqualifying medical condition but cannot get a waiver because somebody's opinion prevents them from getting the waiver for entry