Comment by tptacek

It doesn't. The concern is that all of these assertions are captured by the browsers, who are given custody of the signed assertion as part of the SAML POST flow. The attack being contemplated here is that you have a SAML IDP configured for Cat Sharing Application and for Internal Admin Application; a attacker's browser holds onto the Cat Sharing Application assertion and feeds it to the Internal Admin Application, and, because SP SAML libraries are terrible, the Internal Admin Application honors it.