The manager is correct, it is Private Property, and as such does not have to allow the carry of firearms on the property. When you signed up for Costco, you signed a document stating that you agreed to Costco policies, one of which is that weapons are not allowed on the property, open or concealed. Yes, he was nice to let you continue to finish your meal, and he was also nice in that he could have revoked your membership right there. It has been well documented what Costco policies regarding firearms is. If you do not agree with those policies, then you have a right to not shop there, same as I choose to not buy a pair of Levi's for their anti-gun stance.
He replied that policy is policy "this is private property". I replied that I thought that I was in America, not California. He replied: "well, what difference does it make what state?" I politely responded: "This is an Open Carry state.". He reiterated that it was policy. He mercifully allowed us to stay and finish our meal.