I am having the following error that I havent seen before: 

**System.VisualforceException: Update access denied for Contact, controller action methods may not execute**

I am using a customer controller.

	public without sharing class TestController {
		public Contact myCon {
			get {
				myCon = [SELECT Id, Name, FirstName, MobilePhone FROM Contact WHERE Id =: '003N000000SDkc6'];
				return myCon;
			} 
			set; 
		}

		public TestController() {	}

		public void test(){
			System.debug('@@ ' + JSON.serialize(myCon));
			update myCon;
		}
	}

an a Visualforce Page:


    <apex:page showHeader="true" sidebar="true" controller="TestController">
		<apex:form>
			<apex:inputText value="{!myCon.MobilePhone}" />
			<apex:commandButton value="save" action="{!test}" />
		</apex:form>
	</apex:page>

The page is in a Salesforce site. I know that sites has limition with editing, but I have similar code in other orgs, and I have been able to update opportunities. 

I dont know what I am doing wrong or if there is an extra set up in the site that I am not aware off?