Not only had Carter Page been in contact with Russians at the direction of the CIA, but he had also--as recently as 2013--been doing so at the direction of the FBI itself. He had been a cooperating witness for the FBI in a very important case against Russian IOs--one which, unlike virtually all other such cases, actually resulted in a prosecution. That case culminated in early 2016, just before Page joined the Trump campaign. It might be one thing for the FBI to somehow misunderstand and misrepresent Page's relationship with "another government agency," but how to explain away such a misrepresentation of his relationship with the FBI itself?
This guy gets it:
What are the chances that a couple of months after the Buryakov spy ring is busted in the Spring of 2016, the Rooskies would make Carter Page, the guy who busted said ring, the linchpin of the world’s most audacious double-naught spy caper?
Really. Think about that. The whole thing is ridiculous.