Here is another data point:
Flew to SFO yesterday for a meeting with a client with the intentions of staying for a little vacation. Decided last night o head back home so I purchased a K fare SJC-SLC-JFK departing at 10:30 am. Woke up later than I should have so was able to co-terminal change to OAK-LAX-JFK at 10:20 Am. Booked in K fare and upgraded in both legs.
I tried to make this change via Twitter to save time (so it could be done while I was rushing to leave) and they gave me some runaround that its a co-terminal change and a fee applied. I called DM line and it was done.