My question involves labor and employment law for the state of: California

I'm in my mid-thirties, and I used to be disabled for an embarrassing reason years ago. I used to receive social security disability benefits. My benefits ended about five years ago when I went back to work. Now I'm asked to fill out some insurance forms for my new employer now that I got through the background check. One form asks if I have Medicare. I have part A of medicare (the kind that is free and lasts with you forever). My position is sensitive and required a thorough background investigation. I don't want to put it down because I'm afraid I'll be fired. Plus it will be embarassing. I know I'm mentally capable of doing the job well and safely.

I feel like Medicare and these benefits have ruined my life. Is there a way to disenroll so this doesn't happen again? Should I fill out the health insurance benefits with Medicare info and risk being asked about it and possibly fired? Should I leave it out and possibly be fired down the road?