Most likely, he did not get a dishonorable discharge but rather a General Discharge under less-than-honorable conditions. To have been faced with a dishonorable discharge would have surely forced the weasel to fight it, when under the then-present times would have been more favorable to him.
A General-under-less-than-honorable was still a stigma, but one that he could live with.....until the bastard-from-Georgia allowed him to covert it to HONORABLE
I think you are correct about there possibly being general discharge for Kerry. I read earlier today that a "dishonorable" would require a court martial. I can't substantiate that but did a search on FR for the source but turned up nothing.