The page needs some code examples. It's just marketing talk, needs to be more oriented to it's audience.
A good first question to ask about a data model is, "where does the data live?"
In general, we think it's a good idea to make Stripe the "one true source" for as much of your customer and billing data as possible.
Our company went the opposite way, we have our own model and we abstract stripe as a payment option supported. Recently with the same model we were able to add Paypal and other country specific payment methods.