I picked up a FA a couple of days ago and wanted him to move his base to Tokyo to use him as a sparbot - I did it with my own private jet, and i'm pretty sure that I checked the "move base" option, as it filled up my entire plane (5 seats) just with that one guy, plus i got this feedback in the mail :
" Yrjo Jarvinen had a very pleasant and uneventful flight from London to Tokyo. Although sad to leave his friends behind, moving on a private jet made him more excited to face the challenges in his new home town!"
Problem is, as you can see there : http://www.mmatycoon.com/fighterprofilemanager.php?FID=48334
... his base hasn't changed!
The same shit happened to me a few weeks ago, and i tought i made a mistake (had to pay for a base change a second time), but this time this is prettry clear that something dosen't work...