You can make the payment directly to that address, but their internal ledger system generates some kind of code or invoice that gives you proof that you made the payment and it also validates your payment and then activate your subscription after you did the payment via their service.
So how do you make that direct payment and then trigger the whole validation thing to activate your subscription or have proof that the payment was done? (I think most of them use this system, because it leaves a paper trail for auditing and tax purposes)
It is all triggered simply by
THAT address receiving
THAT many satoshi's. It has nothing to do with any special magical code or invoice... If I took that payment URL and put it into Electrum (or Bitcoin Core or any other BIP70 compatible wallet) it would still work... all they do is exactly what that website does, connects to the URL and retrieves the appropriate info (ie. what address to send to? how much to send?)
Basically, their "internal system" simply creates a unique deposit address for you to send a specific amount to (and starts a 15 minute timer)... if it detects a transaction is broadcast that pays (at least) that amount to the address within that 15 minutes, then it will become "pending". Once the transaction is actually confirmed on the blockchain (I think it's only a minimum of 1 confirmations... might be 3?
), then it's marked as "paid" and the merchant receives a confirmation from BitPay that the invoice has been paid and to do whatever they need to do (send goods, activate subscription etc).
If you need "proof" that you sent the payment... well, that's what the blockchain is for... the payment is there for all to see. I think that it's handy to decode the BitPay invoice yourself anyway, then you can see the InvoiceID's and MerchantID's, addresses and amounts etc... so you have a record of those too!
Also, Why is your post formatting all weird? With extra line breaks etc? Are you doing that on purpose?