The colleague assigned with the task of desymbolicating the crashes reported by BugSense eventually came to the conclusion that this doesn't seem to be possible. In fact, the stacktraces reported where... confusing, to say the least (I don't have an example at hand unfortunately because they store the data only for 7 days). My colleague's solution was easy: switch to Crittercism.
I hesitated to do the switch, because I'd never heard of Crittercism before. Anyway, we went for it and I had the pleasure to integrate the Crittercism SDK in our Android SDK / app. A few minutes later (literally!) everything was ready for the first bug report. What was shown to me on the Crittercism dashboard was stunning: detailed information about all running threads when the crash occured, memory usage, battery level, disk space, sdcard space, all kinds of information about the device, network requests (!!) and the best feature a bug reporter could ever have: logcat (only on Android; optional opt-in feature). Seriously, this is just amazing.
On BugSense we have... well, there is actually nothing BugSense offers Crittercism doesn't (information-wise). One thing I like about BugSense though: their pricing model is much more forgiving. For my app, OpenDocument Reader, I'm still able to use a Free-plan, although we have hundreds of thousands of active users. With Crittercism we'd be forced to upgrade to a paid plan already, because their plans are priced by "monthly active users". The free plan, for example, only allows 30k such monthly active users.
TLDR; Crittercism offers so much more insight into what was going on while the user experienced a crash, but if your app is "too popular" you will be forced to upgrade to a paid plan.