Hey! I am in the Navy Reserves. You were technically enlisted. Were you officially discharged? Also did they slip you into IRR of the Reserves to fulfill your obligation? I know of a sailor who practically did the same thing as you and found out years later they were still in the Navy. They were never discharged. Guess where this person is. You got it - Iraq. They were recalled since they were still technically in the Navy.
I know my story is a Navy story; however, military is military at this point. I would list it as service and explain what happened. If they ever did a background check of any sort, military will be the first thing on the paper.
Just my opinion.