I received a General Discharge for a "Pattern of Misconduct". I received write ups for things like "Not yelling loud enough during formation", "Missing a Spot While Shaving" "Forgetting to fill my Units Canteens during training". Even once I received a write up because I took my newborn to his doctors appointment after giving my unit Two Weeks notice.
Upon receiving your application for benefits the VA will make an initial determination regarding the character of service. It doesn't sound like that will be an issue based upon the facts provided, however, be aware that those determinations are appealable. The below linked article into today's NYTs gives a good account of the military's upgrade of discharge process and the effects on entitlements. The attorneys who responded to your orginal question can provide further guidance on that process.