I enlisted with a BSN. I also know 2 other guys who enlisted with BSNs but they're reservists.
I think your recruiter was probably steering you in an odd direction but regardless, you can still go for HM if you'd like. I was offered that when my recruiter's chief found out that I had a BSN. I didn't want to go in as an HM though. I also think it's whatever is available at the time offered and/or time of re-rate for drop-outs. I've met Nuke drop-outs and sub school drop-outs who got re-rated into many different jobs and most of them had to take whatever was available at the time. But as far as conflict of interest, I think it all depends on timing and what's open at the time. HM is generally manned or overmanned.
Good luck with your endeavors!
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