This formula is not actually a Basal Metabolic Rate (BMR) formula, even though it states BMR. It is actually a Resting Metabolic Rate (RMR) formula, and BMR and RMR are not the same. There can be a 10-20% difference in calories between BMR & RMR. RMR is higher, so if Apple (and many other apps and devices) are using RMR as BMR then they will over-estimate calories per day.
Here are the references for these:
Harris-Benedict equation actually RMR, not BMR: https://www.andeal.org/files/Docs/Frankenfield_et_al_2005%5B1%5D.pdf
Best practices for measuring RMR: http://www.ncbi.nlm.nih.gov/pubmed/16720129
BMR & RMR differences, from the Institute of Medicine, Dietary Reference Intakes For Carbohydrate, Fat, Fiber, Fatty Acids, Cholesterol, Protein, and Amino Acids (pg 112).
http://www.nal.usda.gov/fnic/DRI/DRI_Energy/energy_full_report.pdf
"BMR is commonly extrapolated to 24 hours to be more meaningful, and it is then referred to as basal energy expenditure (BEE), expressed as
kcal/24 h. Resting metabolic rate (RMR), energy expenditure under resting conditions, tends to be somewhat higher (10 to 20 percent) than under
basal conditions due to increases in energy expenditure caused by recent food intake (i.e., by the “thermic effect of food”) or by the delayed effect
of recently completed physical activity (see Chapter 12). Thus, it is important to distinguish between BMR and RMR and between BEE and resting
energy expenditure (REE) (RMR extrapolated to 24 hours)."