If you read about the early founding of PayPal you will find one of the big issues they faced was fraud. I hope they give that angle enough thought otherwise they are going to start leaking cash like the Costa Concordia took on water.
It will only be later that we'll find out what happens behind the scenes. For example Paypal works wonderfully right up until they decide to hold your funds while they investigate. Stripe will probably end up doing something similar and also have similar collateral damage (false positives).
The Stripe FAQ includes a chargeback section which would cover the other likely scenario - people claiming not to have received the item/never made the transaction/it wasn't what they ordered etc.