I wrote to Admirals club through their email address on the website, and here's their reply:

Mr. Fung,

Effective July 1, 2003 the transcontinental flight club access was changed. First of all it must be transcontinental NON STOP to gain access to the lounges. Perhaps the information below will help you to understand the new policy.

-------------------------------------------------------
. ADMIT POLICY
.
EFFECTIVE JULY 1, 2003, PASSENGERS DEPARTING ON
NON-STOP TRANSCONTINENTAL FLIGHTS ARE INVITED TO ENJOY
THE ADMIRALS CLUB, OR FLAGSHIP LOUNGE WHERE AVAILABLE,
PRIOR TO FLIGHT. PASSENGERS MUST BE CONFIRMED IN
FIRST CLASS INVENTORIES F AND Z ON TWO-CABIN SERVICE
AND PREMIUM CLASS INVENTORIES IN P AND Z INVENTORIES
FOR THREE-CLASS SERVICE. THESE CLASSES WILL APPEAR ON YOUR TICKET.
.
REVENUE TICKETS - F OR P
PLANAAHEAD MILEAGE FIRST/PREMIUM CLASS AWARD - Z
AANYTIME MILEAGE FIRST/PREMIUM CLASS AWARD - F OR P


. TRANSCON MARKETS
.
THE TABLE BELOW IS NON-DIRECTIONAL. ACCESS IS VALID IN
EITHER DIRECTION.
.
. BOS LAX
. BOS SAN
. BOS SEA
. BOS SFO
. BOS SJC
. EWR LAX
. FLL LAX
. IAD LAX
. JFK LAX
. JFK LGB
. JFK OAK
. JFK SAN
JFK SEA
JFK SFO
JFK SJC
JFK SNA
LAX MCO
LAX MIA
MIA SFO

You should have had lounge access in SFO and JFK because that was a trancon NONSTOP flight and you were ticketed in the correct inventory. Your ticket will designate the correct accessible inventory. However from SFO to Chicago you would not have access to the lounge as it is not considered a transcon flight because it was not NONSTOP.

I hope this helps to clarify the issue for you. If you have an additional questions, please ask.

Regards,

Admirals Club - HDQ