That does make sense. However, if Paxum is able to handle the added verification costs + insurance in their given fee structure, then surely an exchange could as well. It may be that for the time being nascent bitcoin business don't have the expertise and connections of a Paxum to handle all of this, so they need to 3rd party that.
In theory, yes, but this is very difficult in practice. Unlike most other businesses, you can complete your transaction with an exchange in minutes -- get in cash, buy Bitcoins, and irreversibly ship them out. If the incoming funds weren't good, there is no recovery for the exchange. And the stolen money can be across the planet in minutes. So it's a choice target for fraudsters.
A bitcoin exchange that tried to do this themselves would have to have the very most advanced fraud controls in the financial industry, because they'd be the perfect target. And balancing out all those costs, they'd have only the volume of their share of the bitcoin market.