Why do the MBR partition entry and partition filesystem disagree on the number of sectors?

I've got an SD card used for booting a Beaglebone Black. I was having problems booting from the card, or any card for that matter that I created, and I finally tracked down the problem to a disagreement in the number of sectors in the boot partition. What I mean is, dumping the MBR with dd and checking the first partition entry, the Number of sectors in partition gives 0x40000. This is also what e.g. GParted reports. Then, dumping the FAT16 boot partition, the Large number of sectors is only 0x3fff8. This is a difference of 8, which happens to also be the number of hidden sectors reported by the partition (despite being at offset 2048). But why? The boot ROM seems to be throwing its error because the two numbers don't agree, and I didn't think hidden sectors were even considered in the vast majority of cases, let alone when determining the number of sectors. What gives?