I guess that would work as well, though having the PSDs can still prove the buyer purchased the work. You get the content that you paid for (and that's why it is important to list terms ahead of time as a designer if you will provide PSDs or not. Most people here would assume you get PSDs if you are getting exclusive content made, especially for larger designs such as websites, splash pages, etc). Anyways, the artist themselves will have the PSD as well, and if needed, timestamps can be kept, taking pictures of previews and messages sent/replied between designer and buyer, and so on. There are ways to prove you are the original artist even if the PSD is provided. And I can say, most buyers would like to have the PSDs (not just for the sole reason that they are the original buyers - for editing's sake regarding buttons, etc). Some buyers want to use the same/similar designs for two or more servers (have seen that before) and need to make the appropriate changes to the design. So, the artist should mention ahead of time if this is allowed or not, or else buyers would assume they can since they are the ones who bought the designs (while leaving the credit of course ;D).
As for the invoice, it depends on what name the designer uses (if it is his/her real name, it may be harder to deal with this unless the designer has revealed his/her full name somewhere). There are some people in the world who would have the same names as well~ Furthermore, names can be made up easily with Paypal, etc - still doesn't feel like real evidence, especially when it comes to the RO scene. There have been fraud cases after all, noted with YHMWHY as an example (people trying to copy their names, and whatnot). But of course, that's the buyer's fault if he/she is not careful about the purchases. [You can easily create an account that mentions the designer's name, etc, thus rendering invoices and contracts useless unless the designer has posted somewhere about details of their payment account. But for some/most cases, the designer would mention that in PMs and not in the public for viewing, such as their Paypal account email in particular. This is a true example.] And, having an invoice as proof isn't necessarily good if you're dealing with RO designs XD... since we are dealing with private game server-related content. But, this is getting too much into the legality area.
All in all, it's up to the artist to decide on his/her course of action - and the group of potential buyers will also differ depending on the terms.
Edit: Sorry for the spam, I am high on Soy Milk.