Custom job and site enumeration error

Question

I have a WebPart where I'm executing a custom job. For most users it works fine but for some not, and in log I can see such an entry:

site enumeration stack at microsoft.sharepoint.administration.spsitecollection.get_item(int32 index)

Here is the implementation of Execute method:

public override void Execute(Guid targetInstanceId)
{
            SPWebApplication webApp = this.Parent as SPWebApplication;          

            SPList myList = webApp.Sites[0].RootWeb.Lists["myList"];
            ...
//operations on that list, updates too
}

Under what account is that job executed? Could it be the problem that some users do not have privileges and even webApp.Sites[0] could not be evaluated?