You can be as stubborn as you like, but if you want to go to med school you need to make friends with the ideas that there are reasons for things, and that you don't get a vote on how things work until you're on the other side of med school. Premed advisers don't make the rules, they follow the rules. To get into med school you have to demonstrate your ability to jump through hoops put up by others. There are years and years of jumping like a Jack Russell before you get put in charge of any hoops.
You say you want to get some "bio/chem time" done this summer, presumably so you can get done at CCNY faster. But have you done the work to see if that's even possible? Not because somebody "lets you" but because classes aren't offered every semester and the course content in prereqs doesn't come at you in the same order at every school. It's your MCAT score on the line if you miss content.
If you want to be curious and rigorous and take charge like a grownup, then:
1. Figure out the course sequences at CCNY for bio/chem/ochem/physics and when they're offered.
2. Find the syllabi for the classes you need at CCNY, and find the syllabi for the classes you want to take this summer.
3. For extra credit, get the MCAT content list, which serves nicely as the national syllabus.
4. Make your case: do the work to see if the classes you'll take this summer line up by syllabus with CCNY, and if your overall plan to complete the prereqs is valid. (This is the part that you seem to be expecting somebody else to do for you. It's your job if you want that burger without onions.)
5. If you have a valid case, politely and respectfully bring it to CCNY and ask for consideration of your plan.
tl;dr: gotta know the system to beat the system
Best of luck to you.
