What does less than one count from an x-ray detector mean? (Swift BAT detector)
I think there is a missing piece of information. The BAT is a coded mask telescope. The imaging is done by photons passing through a mask and falling onto an array of 32768 detectors. http://swift.gsfc.nasa.gov/about_swift/bat_desc.html

The "mask-weighted" light curve is produced after a complex ray tracing exercise using an estimate of the position of the source. Looking at some of the software specifications (eg https://heasarc.gsfc.nasa.gov/ftools/caldb/help/batmasktaglc.html ) it seems that the count rate is divided by the number of active detectors.

So in this case it looks like the detection rate was more like 200,000 counts/s in the peak 2ms of the event. There would be 400 detected counts, assuming there are no other corrections for sensitivity or vignetting. However,  I think there probably are - the mask must take out about 50% of these counts and there are gaps between the detectors. A background rate has also been subtracted. So overall I guess that the first point in the burst is due to around 100 detected photons, and so on.