In 2003, small brushless DC motors were way less mature and available as they are now, particularly for low-speed/high-torque applications*. Brushless controllers are much more complicated than brushed controllers, particularly on the control software front, so sticking with simpler and more reliable brushed controllers for a space application makes sense (remember, it probably needed to be radiation hardened - doing that for an H-bridge is much easier than a BLDC controller).
*A notable example of this is in the world of RC cars, where rock-crawlers only very recently have started switching to brushless motors using field-oriented control to deliver acceptable very-low-speed behavior. Until FOC controllers became available, brushed motors offered much better low-speed handling.
Without disagreeing with your point, would availability be an issue in this case? They need one or two, have an enormous budget, and if the technology exists can make their own.
Availability is often strongly correlated with technical maturity. Small brushless motors with FOC didn't become widely available and mature until really the late 2010s. Arguably the foundation of nearly all of DJI's product lines is due to their early mastery of small brushless motor control (drones, gimbals, lens controls, robots, etc), and that's a company founded in 2006, well after the events of the article.
You can get good control of brushed motors with just a couple of transistors. Good brushless control means FOC, which really requires a fairly capable microcontroller in addition to all the power electronics for variable-frequency drive. While brushed motors certainly have limitations, those were quite well understood by the early 2000s (to the point here that assessing whether or not damage had occurred was "just" a question of "have these few transistors suffered from voltage applied in an unintended manner"). Brushless motors involve way more components with way more integration required to make then small. Far more complexity and potential failure modes need to be understood.
*A notable example of this is in the world of RC cars, where rock-crawlers only very recently have started switching to brushless motors using field-oriented control to deliver acceptable very-low-speed behavior. Until FOC controllers became available, brushed motors offered much better low-speed handling.