We know that we can only see ~13.8 billion light years into the cosmic microwave background. But, I have not once read a source saying, "The actual space is expanding at the speed of light in the outer reaches of the universe".
Source?
Metric expansion of space - Wikipedia, the free encyclopedia
I guess i should not have stated it as fact.
We observe the universe expanding faster and faster as we look outward, more red shifted. Since there is no theoretical reason why space cannot expand faster than the speed of light, the assumption is made.
This link explains much of it.