I'm wondering if the code used to generate that address on the fly for the current user is open source(php code I guess?). It seems quite useful since it creates a new address per each user, and also apparently it executes some action whenever the payment is made. It seems to be a simple Bitcoin checkout, which could be great in certain use cases.
You want to use this code for some other forum or what?
I don't think this feature needs to be open source and inspected by everyone, even if forum software is open source it can probably use other extensions with closed source code.
It's not like members are sending millions of Bitcoins every day for copper membership, it's more like symbolic amount, currently that is around 0.00080198 BTC or $24.