Hi Lunar,
Sorry for the delay - our development team have updated with the following:
I took a look and our API indeed makes the paymentMethod field mandatory. So the documentation is wrong, I just updated that api doc page to be a bit more accurate.
It looks like this is not a recent change, that's how it always was ever since 2009. I'm not 100% sure if this should be indeed mandatory or not, but I think we shouldn't change it.
As for getting a list of valid payment method values, they need to log in to the account which they want to use the API with, and go to Money > Payment methods. These are the valid payment methods, but the API requires their IDs and not the names. To figure out the IDs, they can check the delete links in the last column. Each of those URLs have a payment_id parameter, and the API requires one of those IDs.