Since all appointees to this committee must be agreed upon by the Executive Branch as well as both minority and majority leaders from each party (hence 12 from Congress with the Presidents approval/recommendation) and 3 from the President, yes the Executive branch could very well determine what health options are available too you.
The real issues before us now are.
1) why can the Secretary of Health and Human Services even refuse to divulge enrollment numbers? 2) why is the same not keeping the President fully aware or made aware of the problems the site faced before launch and after (conspiracy advocated claim the President knew) 3) By regulating what must be covered and not covered they are deciding what you can have and have not. Remember, there are a lot of gray areas in the law which the Secretary has shown more than enough interest in creating actual rules.