Tossing aside that Assange didn't actually make this statement: In 1996, the possibility that the NSA was sniffing the Internet was largely considered "tinfoil" even by most tech experts.
In 1997 I was working at a company where we built and delivered all software by SUn and many other companies.
We had a Cisco 3640 that I inherited when I got there and I needed to recover the password.
I hired a CCIE to come in and walk me through the recovery and rebuild of this and the other Cisco gear I had at the time.
During the hours that we spent rebuilding the network, we talked a lot about security in general, cisco in specific, and I recall him telling me then "Cisco is required by the NSA to provide them a backdoor into all our routers".
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In 1997 I was working at a company where we built and delivered all software by SUn and many other companies.
We had a Cisco 3640 that I inherited when I got there and I needed to recover the password.
I hired a CCIE to come in and walk me through the recovery and rebuild of this and the other Cisco gear I had at the time.
During the hours that we spent rebuilding the network, we talked a lot about security in general, cisco in specific, and I recall him telling me then "Cisco is required by the NSA to provide them a backdoor into all our routers".
This is not a myth. He was probably referring to the CALEA backdoors. You can Google for "cisco calea 6500" and obtain some public documentation.
It's more likely the FBI would actually interface to it and give said data to the NSA. But your point stands.
The NSA doesn't seem to like to directly interact with ISPs and corporations, so they have the FBI act as their public face, so to speak.