You are right, they can in some cases do that. But it's like the point made by the person who said they would use PayPal, yes in some exceptions they would. But why do you think they go to the wire transfer places in the first place? Because it allows them to anonymously/quietly wire money back in a convenient way without detection by the authorities.
As for paypal, how do you set up a paypal account and send money without a credit card or bank account? How do you get a credit card without a bank account?
I guess another question is can you deposit money in a foreign bank account from within the US?
I've taken a couple vacations to Mexico and one to Belize. It was very easy to withdraw money from my bank account while I was there, but I never tried depositing money.
If illegal immigrants can simply use an ATM to deposit money into a Mexican bank account with an ATM card from a Mexican bank, then that's yet another way around this.