Battery replacements are likely not random. More likely that if the dealership you purchased from has all of the equipment required to perform the replacement, they are the first to get the batteries and then they will start calling their customers (working down their list).
I suspect that if you purchased from a dealership that doesn't have the equipment, you will be waiting awhile. Most of this wait is likely while the dealership waits for the equipment to show up to do the swap (if it is even financially in their best interest to order the equipment, dealer decision).
If you purchased from a dealership without the equipment, I don't see the service department making the effort to call another local dealer with the equipment and line you up for a replacement. Dealerships have always made money on service this will not have changed. Your dealership will not want to send you to another dealership for this service as you will likely never come back to them.
UNLESS....you make a huge stink and they just want you to go away....That is what I did, and they sent me to another dealership. Service manager at my original dealership told me that they had to transfer the warranty claim paperwork over to the other dealership. Follow the $. Still waiting to hear about when the battery will be swapped.
