I went through that whole "can you eat...?" thing many years ago when I became vegetarian too and used the same explanation that you do. BTW, moms just don't get it...it's some kind of universal law!
When I first explained about the McD WOE to her, which I took up because of arthritis, she kept insisting that I was "on a diet," i.e. that I was trying to lose weight. I keep telling her that I'm not "on a diet" I just eat healthy, but have recently given up. I just nod and say, "Yes, I'm on a diet, about 30 more pounds to go..." (I'm 6'5" and 175, so that's just a joke to freak her out...)