I'm a little befuddled on what reason the Navy could possibly have for saying no to a part time job. I worked in a dive shop as a Marine in the fleet. I didn't need to, just wanted to. I was in a traveling singing group for a year in college and also taught an 1100 level Physics lab for a semester, and still kept up a full course load and PT schedule, and I'm getting paid way the hell more by the Marine Corps than any BDCP'er. I think your recruiter is talking out his ass, otherwise it would have been in the paperwork at MEPS as a Statement of Understanding.