Payment Methods

I've recently done two small consultancies - one for an agency of the Cyprus government and one for a US government agency. The Cyprus people asked for my banking details and will make an electronic payment to my account (which happens to be in the US). This is the normal way of doing business in most of the developed world. The US people ask me to submit an invoice which doesn't include any banking information. So I guess they will send me a paper check all the way to Australia, which I will then have to mail all the way back to the US to my bank in New York. Two opportunities for it to get lost in the mail. Here in Australia, paper checks (or cheques in British) are very rarely used. Electronic payment through a number of methods is standard. While the US is on the cutting edge with many communications technologies this definitely doesn't apply to payment methods. Why is this? It seems that Americans think that asking for bank details is a sign of potential fraud. But I can't take money out of an account with just the account and branch number. So why would that be? And why aren't Australians worried about that?