Did I get this wrong?

[shilsen]

No one finds it bizarre that drawing a weapon that doesn't threaten has no bearing on provoking AoOs?

I've always envisioned drawing a weapon (like a sword) as a potential strike; so not provoking an AoO makes sense. But drawing a bow?

No, it isn't bizarre for me. You're assuming that the "no AoO for drawing a weapon" is because it's a 'potential strike', which is an assumption there's no rules support for. I think it's simply a case of the designers thinking that drawing a weapon is easy enough to do without drawing an AoO. Simple.