Yep, they check the bags pretty well at the security checks and we bring in all kinds of food (lunch for 5 of us, plus snacks) and water bottles. Last time we went through the line they were making a couple throw away the glass jars they were trying to bring in (not sure why you'd bring your water in glass jars, it adds so much more weight, but the guy gulped down some of it, then tossed them in the recycle bin).
If you ride the tram they ask in the message that you eat outside food in in the picnic area outside the gate. I think this is more so you don't take up a table in the dining areas that a paying customer could eat at. We just found a bench or quiet area to sit on the ground, it was never a problem.
Alyson