At the risk of being even more confusing and, of course, boring everyone to tears, let me make the following three points:
1. What is legal or not-- I don't personally know what is legal or not with regard to BYOB policy in Chicago. I know what the lady at the Chicago Liquor Control Board told me. As far as I know, the issue has not been tried in court to test the limits of the statute or ordinance, nor do I know what the City's policy of enforcement is, if in fact they have one.
2. Why I think she may be right-- I think she may be correct that the ordinance would be interpreted very broad, how else would you prevent an unlicensed establishment from charging $4 for a coke and then "giving" you a shot of rum. This is called the "set up" model, which is what private clubs in states with dry counties and certain fraternal organizations; e.g., North Carolina or the Elks Club, each patron keeping a bottle at the club for his own use and charged only for a glass of ice and soda.
3. Why I think she may have been wrong--unlike a private club bar that is making a profit off of the set up, generally, a BYOB establishment is simply providing an additional service in order to enhance its primary product (food service), by providing glassware, etc. for the comfort of its guest. You could theoretically bring in your own steak and ask the chef to cook it up for you. Nothing is illegal, the booze is not procured by the establishment, you are simply paying for service. However, again, I see a problem in the way of complaints from licensed establishments if a restaurant becomes too successful in this type of service.
...and, by the way, an establishment can skirt the whole corkage issue by simply stating on its menu or in another conspicous place that it will charge a service fee for any product brought in and consumed in the restaurant. Yes, you must pay all service charges, including gratuities of which you have notice (although I think it is a sin to tip on tax).
FYI, The Harold Washington CPL has copies of the following:
Hotel, Restaurant and Travel Law: A Preventive Approach
Law Reference KF 951 .C6 1997
(Morris/Cournmeyer, 2003; amazon.com $69.79 used)
Looks to be textbook for law classes.
Understanding Hospitality Law
Mugar KF 2042 .H6 J43 1990
(Jefferies, 2000; amazon.com $32.92 used)
Hospitality Law: Managing Legal Issues in the Hospitality Industry
(Barth, 2005 at Wiley.com $75 NEW EDITION)
Unchain your lunch money!