Rather than using an overlay to create your border, use a background. This way you can make sure it's always outside of the object you're bordering, and always exactly 1px wide:
Code:
local bg = object:CreateTexture(nil, "BACKGROUND")
bg:SetPoint("TOPLEFT", -1, 1)
bg:SetPoint("BOTTOMRIGHT", 1, -1)
bg:SetTexture(0, 0, 0)