By using an iframe you make sure that they do not get access to any information on your page - much less the users session cookie.
Instead, if you use this service, you're trusting another 3rd party site to be available and to not be compromised.
I know it is shocking to many of you to hear this, but the data Stripe collects is not really the most sensitive information on the Internet.
The point of the iframe is to contain the damage from any possible compromise. If PAYMENTIFRAME.COM is insecure (heh), you still aren't going to lose user sessions to your actual application.
In fact, their tutorials are so well written and their signup so frictionless that I'd say that any interested website creator should have little trouble setting up a form actually using stripe instead of an iframe.