The response, as the pp noted, does seem inflammatory. I get that you are understandibly upset, however, I would state things in a slightly different way.
"Thank you for your email. I appreciate your inquiry, and I welcome the opportunity to assist in finding a solution for this unit wide issue. For me, I find that I am busy with my patient load, and unable to get coverage to take a half hour lunch." If you are a union hospital, speak to your rep.
People who sign out for a lunch and continue working are in a couple of violations in some states (This is not legal advice, per TOS, however, just as I understand it)--HIPAA as when one is clocked out they do not have a "need to know" (the same with nurses who clock out for the day but then continue to chart off the clock past their shift) and if a situation occurs with a patient, or nurse is hurt that type of thing and a nurse is clocked out, it is probably not in ones best interest to say that "well I clocked out, but I really was not on a break". Wrecks havoc on one's malpractice insurance
I would end the email with suggestions--maybe that the charge nurse covers for all nurses who need a lunch, and each break is scheduled at the begining of the shift. Or at the begining of the shift 2 RN's are partnered and cover for each other on meal breaks.
Look at this for an opportunity to change the current practice, and your NM wants your input. I would also add that you are willing to meet with her to dicuss it further. Again, if you are union your rep is going to want to know about this, and can help you to make changes to the current practice.