I think you misinterpreted the quote. Here it is in full:
To explain, for example, how the universe could have smoothed itself out to achieve the uniformity of temperature that we observe today in the cosmic background radiation, one finds that in the context of the standard Big Bang theory, it would be necessary for energy and information to be transmitted across the universe at about a hundred times the speed of light.
In a nutshell, the universe is isotropic and homogenous - it's basically the same on large scales - and the cosmic microwave background appears to be uniform. In the original Big Bang model, information would have to have been transmitted faster than light.
Inflation solves that problem - indeed, the idea that the entire universe would somehow have been in causal contact was one of the reasons Guth proposed inflation in the first place!
Inflation is not the source of this problem; it is the solution.