I agree this would be the med school's perspective. But it's been my experience, at least at my institution, that grad schools get bent out of shape when they learn of a simultaneous med school applications, as they automatically (probably correctly) perceive themselves to be the distant second choice.
And if your recommendation letters get mixed up, or a confused recommender accidentally mentions med school in your recommendation to a grad school program, well . . . oops. You could be treated dismissively as not sufficiently committed.
Oh. Well I guess it differs by grad school. I just recently applied to grad school on very short notice this year, as a result I did not have any letters of recommendation collected that were specific to grad programs.
In my case, since I had just asked my professors for letters in pursuit of med school they were all tailored to med schools, I had literally just asked my professors to submit those letters to the premedical committee 1-2 months prior and I did not want to bother then to rewrite and re-submit another letter to grad schools. I therefore called the grad school admissions department and literally asked them if I can submit my committee letter packet in lieu of the 3 required recommendations and they told me it was alright. I did, and I also later got into the MS program (Biochem).
Also, my PS for grad school was more along the lines of how i felt the MS in biochem would eventually help me in the field of medicine and as a future doctor - so it was no secret to them that I was going to be applying to med schools after their program.
Edit: Just to be clear, this worked for me but I don't think it was the best way to go about it. I would recommend actually getting LORs tailored to grad school if possible. I decided to apply to the program 2 weeks prior to the deadline and knew that I would not be able to get any new recommendations prior to that deadline. I therefore had no choice but to tailor the PS in a way that blends med school and the MS together into 1 complete and unified objective (which actually turned out well and summed up my true objectives perfectly) I guess I got lucky?
However, to make yourself the most competitive applicant to your perspective MS program that you can be, my final advice would be to do everything you can to make them sound like they are your one and only at that stage in time. Therefore getting letters tailored to grad school, a PS tailored to how you need their program at that stage of your educational endeavors etc. all help convince them that you are seriously considering their program. Although I don't believe they will discriminate against you for applying to other grad programs, med school, etc. I do believe they will have a problem - if you can't believably articulate that you are giving their program
serious consideration.