Wished for a thinner border

At the time I was finalizing the proof, I asked to have the border as thin as possible. The designer replied the (proof's) border was as small as possible to guarantee no portion gets cut off accidentally. Immediately, I thought to myself, "If the cutting process has a margin of error is as large as the white border, then why do the circular stickers have thinner borders?" Trusting in the designer, I didn't press any further and approved the proof. But then when the package arrived, I find a "Sticker Mule" mule sticker with the border cut very close to the edge of the image. If it could have be done, why did the designer reply the way he did? I am still pleased with the stickers, but they didn't turn out exactly as I wanted.