Re: Not much of a 'Society' more like a faceless corporate.
To be clear, SWIFT's customers (and owners) are the banks, not you, the man on the street. That's why they are a 'cooperative society' (as per Belgian law); they operate for the benefit of their members.
If anyone is being difficult on telling you what the SWIFT fee for a transfer is, it'll be your bank (possibly because they know they're taking you for a ride). Other banks, like HSBC, are very clear on the costs of a financial transfer between countries. For example, HSBC's SEPA payments (the EU-wide money transfers) are free online, the SWIFT transfers, used outside the SEPA area, can be £4-7 (and that's come down from £14 or so).
That *excludes* any fees the receiving bank charges their customer for receiving international payments (or any commission they charge on the resulting FOREX conversion). Yes, some banks are still assh*les like that (especially in Africa where hard foreign currency is like gold dust).
And then there is of course the case that not all banks choose to be part of the SWIFT system, and thus have to use an intermediary who *is*. Of course that intermediary wants a cut... you think they do it for free? Please. These are banks. *NOTHING* is for free.