Read the primary source rather than the write-up and the two do not agree, so here is what is actually in it.
Dead space is the answer to the missing dose. A fixed-needle insulin syringe holds a few microlitres in the hub and needle after the plunger bottoms out, and on small draws that is a measurable percentage of every dose. Across ten draws it adds up to most of an eleventh, which is exactly the "nine draws from a ten-dose vial" complaint. Luer-lock syringes are worse; low-dead-space fixed-needle designs are better.
Where I think it is weakest: the subgroup findings are the part I trust least — with enough subgroups something is always significant, and these were not all pre-registered.
The narrow version of the question is how to check the arithmetic without trusting a website calculator, since three calculators gave me three answers. I would rather have one careful answer than five confident ones.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.