Your logic leads to the idea of the CIA's/FBI's connections to the ISIS.
1. American nationals fight alongside ISIS
2. CIA's duties are analogical to the SVR, FBI's - to the FSB.
==>
CIA and FBI have connection to ISIS. 
.
Your logic leads to the idea of the CIA's/FBI's connections to the ISIS.
1. American nationals fight alongside ISIS
2. CIA's duties are analogical to the SVR, FBI's - to the FSB.
==>
CIA and FBI have connection to ISIS. .
Please read the articles at #2 and #4. I will answer any specific questions that you have about the content.
It's not a matter of faulty logic. It's a matter of well deserved suspicion with a country that has its hands deep into world wide terrorism.