I think your supplier said that cause they want to be protected against chargebacks. Also, if you think people in the west have it bad when it comes to Paypal, be glad if you are not Asian. If you even can get an account as an Asian, they will lock it as soon as their Bayesian filters pick up any abnormality (like logging on from a new IP).
To the OP. Faking an invoice is real easy. Also, if you are in Europe and if your Paypal is in your real name: do what someone else here stated. Just remind them that they are a registered financial institution. Since they already have your ID-info, ask them to shape the f**k up or you will report them to any financial oversight authority you can find. I've had my share of limitations on Paypal, and have always managed to make them see my way within a couple of days.
Good luck.