As a vegetarian, I would eat the rice or vegetables off a plate, even if it shared the plate with a piece of meat, because to me they are separate entities. I wouldn't normally freak out if the broccoli "touched" the chicken breast. What I've always had an issue with is if it's cooked with the meat. Generally, in something like a stew, that's a no-no for me, the fat from the meat is definitely absorbed by the vegetables or gratins and that's not OK with me. Where I am slightly confused is in a dish where, though the meat and rice/vegetables are cooked in the same pot, they don't mix until the cook mixes them post cooking time. Let's say the meat is at the very bottom, comprising 1/3 of the pot and the rice is on top, filling up the last 2/3 of the pot. The rice at the top (let's say 1/3 down from the rim) has really no contact at all with the meat. It's not a saucy dish (no puns intended) so there's no fat-filled gravy for the rice to be soaked in. Traditionally I will eat this rice. (As a side note, I don't actually make this dish myself, when I go camping with my family, who, incidentally, are not vegetarian in any respect, this is a popular dish that usually gets served and one that is construed with my eating habits in mind.) If I ever decide that this dish is now inappropriate for me, there will be, of course, consequences. Now that I'm trying to move towards veganism, however, I am becoming extremely vigilant of the food that I eat and this has come up for me because I am going camping with my family this weekend. I'll throw in some inevitably disgusting faux-chicken pieces from my local supermarket, grin, and bear it. Maybe we'll have some corn to roast.
And as an unrelated side-note, I found an absolutely amazing online social networking community geared towards the vegetarian/vegan population. It's a must-visit/join: Volentia.com
Happy conscious-minded eating!