If invited to a friend's house for a party, should you assume you have to bring your own food?

I had a first time invitation to a friend's house for what she termed "a picnic." I arrived at the appointed time to find her husband grilling hamburgers and hot dogs. I didn't see my friend, but there was bowls and dishes of food out on the picnic table, so I grabbed a paper plate and started to load up when I heard her voice behind me saying, "What do you think you're doing?" I turned around to see her scowling at me. I told her I was helping myself. She snapped, "Yeah, to MY food!" Come to find out, she assumed I would bring my own food. She was willing to have her husband grill anything I brought that required it, but other than that, I was on my own. I told her that I assumed that, as being the host, she would have provided the food. She said I assumed incorrectly and how could I have thought she would have to bear the expense of feeding me. I had to leave since I had not brought anything and I'm now confused. Is it customary to assume you have to bring your own food to a barbecue if it is not mentioned in a verbal invitation?