Negative. When you are offered a job you select a base from the list of open bases. If you do not want one of them then you must agree to the commuter policy basically saying that you will report to your base (from the list of available gateways) on your start day and it's your problem to get there on time. If you do not want to take the job with those provisions then don't.

However, if you take the job at one of the 30 some open gateways then that is your gateway forever. Even if the company later closes your base you will not be kicked out of the gateway...you are grandfathered.

There is ZERO chance you will be "re-assigned" to some other base. That would be outrageous and is totally not true.